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The present study considers a single-server Markovian queueing system by observing the number of customer arrivals during the service time of a customer. We estimate the traffic intensity in this queueing system along with the average queue length and the expected number of customers in the system. We propose classical and Bayesian frameworks to estimate the parameters of interest. In the Bayesian setup, three forms of prior distributions for ρ and two loss functions are considered. Furthermore, the predictive distribution of the number of customer arrivals during the service time of a customer and the equal-tailed credible region of ρ are obtained. The aforementioned approaches are illustrated with numerical examples based on simulation studies. [ABSTRACT FROM AUTHOR]

Consumers tend to perceive a service of higher value when more consumers, under the influence of others, make the same choice. In this article, we investigate the impact of social interactions in service operations under various price, waiting time target, and capacity decisions. The service is delivered through an M/M/1 queue system which attempts to achieve a waiting time target through a volume-based capacity allocation policy. Consumers perceive a positive (negative) value of the service if the queue length is longer (shorter) than the base queue length – an anchor point in their value perception. We examine the relationship of the intrinsic value of the service and the consumer's value perception (in terms of the queue length anchor point) with the price, the waiting time target, and the capacity decisions. We also quantify the potential gain or loss in profit when the influence of social interactions is ignored. Theoretical results are derived to guide the price, waiting time target, and capacity decisions to exploit the influence of social interactions. It is found that there exist delicate dynamics among key parameters and variables, when ignored, that could lead to undesirable outcomes. The study offers new insights to balance the demand-inducing effect and the congestion-aggravating effect in a service system under the influence of social interactions. [ABSTRACT FROM AUTHOR]

This paper presents a physical space design method for mixed reality-based immersive environments by improving the color rendering of optically visible head-mounted displays. In OST-HMD, the phenomenon that the light of the external environment is combined with the enhanced image occurs, which reduces the visibility of the content. Moreover, previous studies to solve this problem required additional optical components or performed only simple verification. Proposed physical space was designed using black curtains, blinds, low-reflection structures, and adjustable lighting. The physical space can be adapted to the intended use of the physical space through physical transitions for multiple users without additional optics. To verify the usefulness of this environment, we measured the color gamut and intensity spectrum in three experimental environments. Also, we analyzed the factors that change the color gamut according to the components and the surrounding environment. As a result, the color gamut improved by up to 4.7 times from 19.92% to 93.53% based on the environment and improved by up to 4.1 times from 21% to 86.29% depending on the location. The experimental results revealed that the presented method could reduce the factors that degrade the color gamut within all measurement locations and significantly improve the color gamut. [ABSTRACT FROM AUTHOR]

Bounded rationality includes potential cognitive deficits that limit human rational behaviour. In this paper, we allow for estimation errors of their utility and consider bounded rationality in queueing models with retrials. Upon arrival, customers decide whether to join the system based on their perceived utility, and their choice behaviour is characterised by a logit choice model. For a revenue-seeking server and a social planner, we investigate corresponding optimal pricing strategies. We find that the revenue-optimal price is no longer socially efficient in general but depends on the retrial rate. There exists a threshold such that the socially optimal price is greater than the revenue-optimal one when the retrial rate is below this threshold; otherwise, the revenue-optimal price is greater. A larger bounded rationality widens the gap between social welfare under the revenue- and socially optimal prices. Furthermore, the server's revenue may increase or first decrease and then increase with respect to customers' rationality levels, and the server may find it beneficial to reveal waiting time information when customers' rationality is high. Finally, failing to account for customers' bounded rationality can lead a significant revenue loss for the server and the proportion of such a revenue loss is close to 1 as customers become fully boundedly rational. [ABSTRACT FROM AUTHOR]

We consider a tandem queue consisting of two stations. We demonstrate that customer numbers and waiting times at both stations are independent of each other in the steady-state. As an optimal design, in the second station, We consider that there is a single channel that has the total service capacity of two parallel channels instead of two identical channels. Then, we indicate that the optimal system works faster than the tandem queue system with parallel channels at the second station. Also, when the total service capacity is limited, the mean waiting time in the system has been minimized in the optimal system obtained the mean waiting time lower limit. We compared it to those found through a numerical example. [ABSTRACT FROM AUTHOR]

Queueing systems with batch Markovian arrival process (BMAP) have paramount applications in the domain of wireless communication. The BMAP has been used to model the superposition of video sources and to approximate the super-position of data, voice and video traffic. This article analyzes an infinite-buffer generally distributed batch-service queue with BMAP, general bulk service (a, b) rule and batch-size-dependent service time. In this proposed analysis, we mainly focus on deriving the bivariate vector generating function of queue and server content distribution together at departure epoch using supplementary variable technique. The mathematical procedure for the complete extraction of distribution at departure epoch has been discussed and using those extracted probabilities, we achieve the queue and server content distribution at arbitrary epoch. Finally, numerical illustrations have been carried out in order to make a deep insight to the readers which contains deterministic as well as phase-type service time distributions. [ABSTRACT FROM AUTHOR]

We consider an infinite waiting space G I / M a , b / 1 queueing system in which customers arrive according to a renewal process. The server serves the customers in batches under general bulk-service rule. The successive service times of batches are mutually independent and have a common exponential distribution. To obtain the queue-length distributions at prearrival and random epochs, we have used the displacement operator which assists to solve simultaneous non-homogeneous difference equations. An analytically simple and computationally efficient procedures have developed to compute the waiting-time distribution of an arrival customer. Our formula to determine the waiting-time distribution is also useful even when multiple poles occur in the Laplace-Stieltjes transform of the interarrival time distribution. We have determined closed-form analytical expression for the distribution of size of a service batch of an arrived customer. We also have derived the results of some particular well-known queueing models from our model. Some numerical results are provided in the form of tables for a variety of interarrival-time distributions to demonstrate the variation of performance measures of the system. [ABSTRACT FROM AUTHOR]

We propose a new integrated queueing-inventory and reliability model. First, we obtained time-dependent performance measures by using the Laplace transform method. Then, we derived stationary performance measures by using alternative solution methods, including the probability generating function and matrix geometric method. Optimization procedures were developed for both make-to-order and make-to-stock cases. Performance evaluation of the derived time-dependent and stationary performance measures were reviewed first. Then we compared joint replacement and production-inventory control with separate optimization for respective production modes. Finally, the impact of deteriorated services under different demand rates and parameter settings was investigated. Prior studies are neglecting the mutual interaction between production and reliability. This study contributes to filling the gap. In our proposed numerical example, a cost reduction of more than one-third was achieved by joint optimization. The result shows that decision-maker should make his decisions in an integrated manner otherwise the price paid may be significant. [ABSTRACT FROM AUTHOR]

Automated material handling systems play a crucial role in intelligent manufacturing workshops. The main difficulty in optimising buffer allocation in such systems is to provide good evaluation for the performance measures of interest, such as throughput, and cycle time, for customised manufacturing systems. However, existing research lacks an in-depth consideration of the integration of production and material handling systems. Therefore, a flow shop with capacitated batch transports, where the transported batch size depends on the number of jobs in buffers and capacity of transporters, is presented. The system is modelled as an open queueing network with blocking, and an approximation method is proposed for computing the performance measures. Then, an iterative optimisation algorithm embedded with the performance evaluation method is developed to determine an optimal buffer allocation. Finally, the computational experiments are conducted to validate the accuracy and efficiency of the proposed approaches. [ABSTRACT FROM AUTHOR]

We study a queueing system of an unreliable server providing services to customers with two different service rates. When the system is empty of customers, the server takes a vacation and provides a low service rate. Once the vacation is completed, the server is resumed to serve customers, if any, at a higher service rate, or takes another vacation if the server found an empty system. The server is subject to random breakdowns when serving customers and if failed, it enters a repair stage. Under different system information levels, we investigate customers' equilibrium strategies and follow-up system measures. Numerical comparisons among different information levels reveal that when the traffic load is large enough, the service provider (SP) prefers to disclose the server's status and queue length information to customers to maximize the system throughput. While when the traffic load is small enough, there exist two cases with regard to the failure rate: (i) If the failure rate is smaller than a certain threshold, the SP tends to conceal the system information. (ii) If the failure rate is greater than the threshold, revealing the information is helpful to maximize the system throughput. [ABSTRACT FROM AUTHOR]

This paper investigates a discrete-time GI/D-MSP/1/\infty queueing system under N-policy with renewal input. The service process is correlated and its structure is constructed through discrete-time Markovian service process. The idle server resumes to serve the customers as soon as the number of waiting customers in the queue reaches a predefined threshold value N and serves the customers exhaustively until the system becomes empty. We use the matrix-geometric method to derive the system-length distribution at prearrival epoch. Employing the Markov renewal theory, we obtain the system-length distribution at random epoch. We also carried out the system-length distributions at outside observer's, intermediate and post-departure epochs. Further, we find the waiting-time distribution in the queue measured in slots of an arrival customer. An expected linear cost function per unit time is considered to determine the optimal value of N, which minimises the expected cost function. Some numerical results are demonstrated to measure the effects of N, interarrival-time distributions and other model parameters. [ABSTRACT FROM AUTHOR]

In this article, customers' strategic behavior and social optimation in a constant retrial queue with setup time and the N-policy are investigated. Customers who find the server isn't idle either leave forever or enter an orbit. After a service, the server will seek a customer from the orbit at a constant rate. The server is closed whenever the system becomes empty, and is activated when the number of waitlisted customers reaches a threshold. We obtain the equilibrium arrival rates in different states. There exist both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors. Through the Particle Swarm Optimization (PSO) algorithm, we numerically obtain the optimal solution of the social welfare maximization problem. Finally, numerical examples are presented to illustrate the sensitivity of system performance measures. [ABSTRACT FROM AUTHOR]

We analyze the behavior of a particle moving along a d-dimensional lattice and representing a "doubly stochastic" random walk. Unlike the classical random walk, the lattice is randomly generated upon particle's landing at a node. At any time, the particle is enclosed in a rectangular cylinder R = R a × R b (i.e., with a bounded a-dimensional rectangle Ra at its base) it attempts to escape. Thus, the particle moves from one node to another at random epochs of time and, with some probability, leaves R. The particle may jump arbitrarily far beyond the boundary ∂ R at its passage time. Furthermore, the particle's location is not assumed to be known in real time, but only upon certain random epochs { τ n }. Of a key interest is the location A (t) of the particle at any time, where A (t) is the linear interpolation of particle's positions at times τn's. If τ ρ denotes the first observed escape time (virtual first passage time), where ρ = min { n : A ( τ n) ∈ R C } , we target the joint characteristic function of A (τ ρ − 1) , A (τ ρ) , τ ρ − 1 , τ ρ , and A (t) itself, where t ∈ [ 0 , τ ρ − 1 ] or (τ ρ − 1 , τ ρ ] in tractable forms, thereby attempting to enhance as much as possible the probabilistic data lost due to the crudeness of the observations and to couple A (τ ρ − 1) , A (τ ρ) , τ ρ − 1 , and τ ρ with deterministic time intervals [ 0 , t ]. Among various applications, we discuss and treat antagonistic games of two active and several passive players as well as situations that occur in complex queueing systems. [ABSTRACT FROM AUTHOR]

Localising facilities and assigning product flows in a reverse logistics environment is a crucial but difficult strategic management decision, certainly when value decay plays an important part. Despite numerous publications regarding closed-loop supply chain design, very few addressed the impact of lead times and the high level of uncertainty in reverse processes. In this article, a single product reverse logistics network design problem with multiple layers and multiple routings is considered. To this end, a new advanced strategic planning model with integrated queueing relationships is built that explicitly takes into account stochastic delays due to various processes like collection, production and transportation, as well as disturbances due to various sources of variability like uncertain supply, uncertain process times, unknown quality, breakdowns, etc. Their impact is measured by transforming these delays into work-in-process, which affects profit through inventory costs. This innovative modeling approach is difficult to solve because of both combinatorial and nonlinear continuous relationships. The differential evolution algorithm with an enhanced constraint handling method is proposed as an appropriate heuristic to solve this model close to optimality. A number of scenarios for a realistic case illustrate the power of this optimisation tool. [ABSTRACT FROM AUTHOR]

The lot-sizing problem in batch manufacturing systems with capacity constraints is studied using queueing relationships and optimisation techniques. In this research, the effect of lot sizes when there are parallel machines and multiple part types is considered. Furthermore, the issue of whether or not to use pooled queues, based on part types, to feed the machines is examined. Different scenarios are evaluated using GI/G/n queueing approximations to predict performance and optimise lot sizes. Optimisation is based on minimising the mean flowtimes, which include queue and lot service times. The results show that if part types are very different, there are situations in which pooling is not advantageous. [ABSTRACT FROM AUTHOR]

In the literature, it has been shown that autocorrelation in service times has a dramatic impact on performance measures in delay systems. Although some studies deal with systems having autocorrelated service times, a general renewal approximation methodology that can incorporate this information in analytical models has not been previously proposed. In this paper, we develop a discrete event simulation based analytical method to fit approximating distributions to capture the characteristics of autocorrelated service times. Our observations indicate that a single approximating service time distribution fails to accurately predict the behaviour of the delay system. Therefore, we include the server utilization information in the developed method, which, in turn, provides a family of approximating service times. Testing our approximation both in predicting the mean delay and the system size distribution of the original systems with autocorrelated service times show that it can be highly accurate. [ABSTRACT FROM AUTHOR]

A two-tier service system consists of free and toll channels with its toll revenue reinvested in service capacity. In this study, we develop two models with revenue reinvestment in either the free or the toll system. Similar to the congestion problem in an urban transportation network, we investigate whether the Downs–Thomson paradox occurs in the cases where an additional free service capacity is increased. Based on the relations between the major performance measures (such as the customer waiting time, toll system revenue, and total social cost) and the key system parameters and decision variables (such as the traffic intensity, proportion of revenue invested in capacity expansion, toll system price, and service cost of the free or toll system), we find that the Downs–Thomson paradox in terms of total social cost may exist. The findings provide managerial insights if an additional budget is invested to expand the free service capacity. [ABSTRACT FROM AUTHOR]

Stochastic kriging is a popular metamodeling technique to approximate computationally expensive simulation models. However, it typically treats the simulation model as a black box in practice and often fails to capture the highly nonlinear response surfaces that arise from queueing simulations.We propose a simple, effective approach to improve the performance of stochastic kriging by incorporating stylized queueing models that contain useful information about the shape of the response surface. We provide several statistical tools to measure the usefulness of the incorporated stylized models. We show that even a relatively crude stylized model can substantially improve the prediction accuracy of stochastic kriging. [ABSTRACT FROM AUTHOR]

We are considering the problem of obtaining the response time distribution of fault-tolerant multi-tier services. In the provision of software-as-a-service applications, the service provider is obliged to ensure a certain quality of service. Herein, we regard upper bounds on the response time. The services consist of multiple components with different functionality, which are prone to failures, and fail according to a certain failure time distribution. However, due to redundancy, a failure will not necessarily bring the service down, but rather increase the response time. A fundamental difficulty with estimating the response time distribution while considering failures is related to the disparity in the time scales of the time between failures and service times. To overcome this issue, we propose an approach based on a decomposition, which combines an analytic model of the failure process and a discrete event simulation model to sample the response time distribution. In an experimental study, we compare this simulation-based approach with an analytic approach, and illustrate how this approach can be utilised by service providers as decision support. We also show that in certain cases, the analytic approach might provide a safe bound on the response time. [ABSTRACT FROM AUTHOR]

Crowdsourcing is getting popular after a number of industries such as food, consumer products, hotels, electronics, and other large retailers bought into this idea of serving customers. In this paper, we introduce a multi-server queueing model in the context of crowdsourcing. We assume that two types, say, Type 1 and Type 2, of customers arrive to a c-server queueing system. A Type 1 customer has to receive service by one of c servers while a Type 2 customer may be served by a Type 1 customer who is available to act as a server soon after getting a service or by one of c servers. We assume that a Type 1 customer will be available for serving a Type 2 customer (provided there is at least one Type 2 customer waiting in the queue at the time of the service completion of that Type 1 customer) with probability $$p, 0 \le p \le 1$$ . With probability $$q = 1 - p$$ , a Type 1 customer will opt out of serving a Type 2 customer provided there is at least one Type 2 customer waiting in the system. Upon completion of a service a free server will offer service to a Type 1 customer on an FCFS basis; however, if there are no Type 1 customers waiting in the system, the server will serve a Type 2 customer if there is one present in the queue. If a Type 1 customer decides to serve a Type 2 customer, for our analysis purposes that Type 2 customer will be removed from the system as Type 1 customer will leave the system with that Type 2 customer. Under the assumption of exponential services for both types of customers we study the model in steady state using matrix analytic methods and establish some results including explicit ones for the waiting time distributions. Some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

In this article, we analyze the transient behavior of the workload process in a Lévy-driven queue. We are interested in the value of the workload process at a random epoch; this epoch is distributed as the sum of independent exponential random variables. We consider both cases of spectrally one-sided Lévy input processes, for which we succeed in deriving explicit results. As an application, we approximate the mean and the Laplace transform of the workload process after a deterministic time. [ABSTRACT FROM PUBLISHER]

In this paper, we study a discrete-time single-server queueing system where the arriving traffic consists of both delay-sensitive and delay-tolerant streams. We analyze the effects of a reservation-based scheduling discipline on the delay characteristics of both types of traffic. Under this discipline, a placeholder packet is inserted in the queue to accommodate future delay-sensitive arrivals, allowing them to bypass a part of the queue, without suppressing the delay-tolerant traffic. On the basis of a probability generating functions (pgf) approach, we analyze the system state distribution and the delay distribution for either traffic type and present closed-form expressions for the expected delays as well as the tail probabilities of the packet delays. We illustrate the results comparing the delay performance of our reservation-based scheduling discipline to the performance achieved by the traditional Absolute Priority (AP) and First In First Out (FIFO) disciplines. [ABSTRACT FROM PUBLISHER]

TheM/G/1 model is the fundamental basis of the queueing system in many network systems. Usually, the study of theM/G/1 is limited by the assumption of single queue and infinite capacity. In practice, however, these postulations may not be valid, particularly when dealing with many real-world problems. In this paper, a two-stage state-space approach is devoted to solving the state probabilities for the multi-queue finite-capacityM/G/1 model, i.e.q-M/G/1/KiwithKibuffers in theith queue. The state probabilities at departure instants are determined by solving a set of state transition equations. Afterward, an embedded Markov chain analysis is applied to derive the state probabilities with another set of state balance equations at arbitrary time instants. The closed forms of the state probabilities are also presented with theorems for reference. Applications of Little's theorem further present the corresponding results for queue lengths and average waiting times. Simulation experiments have demonstrated the correctness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

All financial practitioners are working in incomplete markets full of unhedgeable risk factors. Making the situation worse, they are only equipped with imperfect information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for sudden and possibly contagious changes in the investment flows from their clients so that they can avoid the over- as well as under-hedging. In this work, the prices of securities, the occurrences of insured events and (possibly a network of) investment flows are used to infer their drifts and intensities by a stochastic filtering technique. We utilize the inferred information to provide the optimal hedging strategy based on the mean-variance (or quadratic) risk criterion. A BSDE approach allows a systematic derivation of the optimal strategy, which is shown to be implementable by a set of simple ODEs and standard Monte Carlo simulation. The presented framework may also be useful for manufacturers and energy firms to install an efficient overlay of dynamic hedging by financial derivatives to minimize the costs. [ABSTRACT FROM AUTHOR]

In this paper, we review some of the methods used to find the number of customers in system in an GI/M/c/N queue for finite and infinite buffer sizes N, and we add some new methods. It was found that with modern computers, most of these methods provide results in a fraction of a second, even for high values of c and N. We also show that the traditional methods for dealing with infinite buffers lead to double integrals, a problem that is avoided by using a novel method we suggest. [ABSTRACT FROM AUTHOR]

Queues with Markovian arrival and service processes, i.e., MAP/MAP/1 queues, have been useful in the analysis of computer and communication systems and different representations for their stationary sojourn time and queue length distribution have been derived. More specifically, the class of MAP/MAP/1 queues lies at the intersection of the class of QBD queues and the class of semi-Markovian queues. While QBD queues have a matrix exponential representation for their queue length and sojourn time distribution of orderNand N2, respectively, whereNis the size of the background continuous time Markov chain, the reverse is true for a semi-Markovian queue. As the class of MAP/MAP/1 queues lies at the intersection, both the queue length and sojourn time distribution of a MAP/MAP/1 queue has an orderNmatrix exponential representation. The aim of this article is to understand why the order N2distributions of the sojourn time of a QBD queue and the queue length of a semi-Markovian queue can be reduced to an orderNdistribution in the specific case of a MAP/MAP/1 queue. We show that the key observation exists in establishing the commutativity of some fundamental matrices involved in the analysis of the MAP/MAP/1 queue. [ABSTRACT FROM AUTHOR]

This paper presents an unobservable single-server queueing system with three types of uncertainty, where the service rate, or waiting cost or service quality is random variable that may obtainn(n> 2) values. The information about the realised values of parameters is only known to the server. We are concerned about the server’s behaviour: revealing or concealing the information to customers. Then-value assumption and the server’s behaviour enable us to consider various pricing strategies. In this paper, we analyse the effect of information and uncertainty on profits and make comparisons between the profits under different pricing strategies. Moreover, as for parameter variability reflected by the number of each parameter’s possible choicesn, we observe the effect of variablenon all types of profits and find that revealing the parameter information can much more benefit the server with the increase ofn. [ABSTRACT FROM AUTHOR]

This article considers the optimal design of unpaced assembly lines. Two key decisions in designing an unpaced assembly line are the allocation of work to the stations and the allocation of buffer storage space between the stations. To the best of the author's knowledge, this is the first article to jointly optimize both the allocation of workload and the allocation of buffer spaces simultaneously when the objective is to maximize the revenue from throughput minus the cost of work-in-process inventory. Exact solutions are provided for small lines (three or four stations) with a fixed kind of processing time distribution (exponential or Erlang). Ten observations are made about the characteristics of the allocation of workload and buffer spaces. Heuristics are suggested for designing lines with more stations or different processing time distributions. A simulation study is done to test the observations and heuristics for longer lines and different processing time distributions (lognormal). Significant savings can be achieved by jointly optimizing both the workload and the buffer space allocations. [ABSTRACT FROM PUBLISHER]

This article investigates methods for reallocation of service capacities in open Jackson networks in order to minimize either a system's mean total work-in-process or its response time. The focus is mainly on a method callednode generation, by which capacity can be transferred from a node in echelonjto a newly generated node in echelonj+ 1. The proposed procedure is compared with the more conventional capacity redistribution method, by which capacity can be transferred from any node in echelonjto existing successor nodes in echelonj+ 1. Formulation of each method as a mathematical programming problem reveals the structure of the optimal solution for both problems. The motivation for considering these approaches stems from real-life settings, in particular, from a production line or supply chains where the two types of capacity reallocation are applied. Heuristic methods are developed to solve relatively large networks in tractable time. Numerical results and analyses are presented. [ABSTRACT FROM PUBLISHER]

Single server retrial queueing models in which customers arrive according to a batch Poisson process are considered here. An arriving batch, finding the server busy, enters an orbit. Otherwise, one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit (the orbital customers) try to reach the server subsequently with the inter-retrial times exponentially distributed. Additionally, at each service completion epoch, two different search mechanisms, that is, type I and type II search, to bring the orbital customers by the system to service, are switched on. Thus, when the server is idle, a competition takes place among primary customers, customers who come by retrial and by two types of searches. The type I search selects a single customer whereas the type II search considers a batch of customers from the orbit. Depending on the maximum size of the batch being considered for service by a type II search, two cases are addressed here. In the first case, no restriction on batch size is assumed, whereas in the second case, maximum size of the batch is restricted to a pre-assigned value. We call the resulting models as model 1 and model 2 respectively. In all service modes other than type II search, only a single customer is qualified for service. Service times of the four types of customers, namely, primary, repeated, and those who come by two types of searches are arbitrarily distributed (with different distributions which are independent of each other). Steady state analysis is performed and stability conditions are established. A control problem for model 2 is considered and numerical illustrations are provided. [ABSTRACT FROM PUBLISHER]

A recent article on bulk-service queues gives a generating function for the steady-state probabilities of the embedded Markov chain for a single-server infinite-space system in which, the customers arrive according to a Poisson process and are served in batches with quorum a and capacity b, and the service time follows a general distribution dependent on batch size. This system is equivalent to the bulk queueing model M/Gj(a,b)/1, whose general solution requires finding the roots of the denominator of the underlying generating function. The article claims that the use of roots may result in numerical inaccuracies, especially for large values of b. Hence it only solves for the finite-space model M/Gj(a,b)/1/(B + b) using (B + 1) simultaneous linear equations. We present a simple way to obtain the probability distribution of queue length at post-departure epochs for the infinite-space model M/Gj(a,b)/1 using roots, then an alternative method to solve the finite-space queue M/Gj(a,b)/1/(B + b). We derive, for the first time, closed-form formulas for the queue-length distribution of models with deterministic service time for both infinite (M/Dj(a,b)/1) and finite-space (M/Dj(a,b)/1/(B + b)) systems. We also show that the queue-length distribution of M/Dj(a,b)/1 can be approximated by a Poisson distribution when the traffic intensity ρ is low. Numerical results are both tabulated and graphed. [ABSTRACT FROM AUTHOR]

We use semi-regenerative, fluctuations methods, and sequential games to examine a queueing system with server performing a secondary maintenance work. When the buffer becomes empty, the server leaves the system to service packets of jobs at a maintenance facility where his time there is restricted by T (a random time). He returns to the system when his sojourn time expires and if the last packet is fully processed. If the buffer contents is below N, the server departs from the system again to continue with maintenance; this time rendering just one packet at a time until the buffer is replenished. We obtain compact and explicit functionals for the queueing process in equilibrium for both discrete and continuous time parameter processes. [ABSTRACT FROM AUTHOR]

No other department influences the workload of a hospital more than the Department of Surgery and in particular, the activities in the operating room. These activities are governed by the master surgical schedule (MSS), which states which patient types receive surgery on which day. In this paper, we describe an analytical approach to project the workload for downstream departments based on this MSS. Specifically, the ward occupancy distributions, patient admission/discharge distributions and the distributions for ongoing interventions/treatments are computed. Recovering after surgery requires the support of multiple departments, such as nursing, physiotherapy, rehabilitation and long-term care. With our model, managers from these departments can determine their workload by aggregating tasks associated with recovering surgical patients. The model, which supported the development of a new MSS at the Netherlands Cancer Institute-Antoni van Leeuwenhoek Hospital, provides the foundation for a decision support tool to relate downstream hospital departments to the operating room. [ABSTRACT FROM AUTHOR]

Litho cells are the most expensive equipment in a wafer fab. To support decision-making on this equipment, accurate simulation models for throughput and cycle time are helpful. The simulation models that are typically developed incorporate various shop floor details. To properly model these details, they should be quantified, which is difficult and time-consuming. In this article, a lumped parameter model is proposed for the litho cell. The model consists of two parts: a detailed representation of the processing inside the track and scanner, and an aggregate representation of the factory floor feeding the loadport. The track-scanner is modelled as a tandem flow line with blocking. The shop floor is represented by a delay distribution that incorporates all contributions outside the machine. Simulation results show that the suggested method provides a simple, yet accurate approximation of the litho cell. [ABSTRACT FROM AUTHOR]

A simulation-based methodology is proposed to map the mean of steady-state cycle time (CT) as a function of throughput (TH) and product mix (PM) for manufacturing systems. Nonlinear regression models motivated by queueing analysis are assumed for the underlying response surface. To ensure efficiency and control estimation error, simulation experiments are built up sequentially using a multi-stage procedure to collect data for fitting the models. The resulting response surface is able to provide a CT estimate for any TH and any PM, and thus allows the decision maker to instantly investigate options and trade offs regarding their production planning. [ABSTRACT FROM AUTHOR]

In this article, we consider a single-server, finite-capacity queue with random bulk service rule where customers arrive according to a discrete-time Markovian arrival process (D-MAP). The model is denoted by D-MAP/GY/1/M where server capacity (bulk size for service) is determined by a random variable Y at the starting point of services. A simple analysis of this model is given using the embedded Markov chain technique and the concept of the mean sojourn time of the phase of underlying Markov chain of D-MAP. A complete solution to the distribution of the number of customers in the D-MAP/GY/1/M queue, some computational results, and performance measures such as the average number of customers in the queue and the loss probability are presented. [ABSTRACT FROM AUTHOR]

A location problem with stochastic demand and congestion where mobile servers respond to service calls originating from nodes is considered. The problem is of the set-covering type: only servers within the coverage radius of the demand-generating node may respond to a call. The service level constraint requires that at least one server must be available to respond to an arriving call, with some prespecified probability. The objective is to minimize the total number of servers. It is shown that earlier models quite often overestimate servers' availability and thus may lead to infeasible solutions (i.e., solutions that fail to satisfy the service level constraint). System stability conditions and lower bounds on system availability are developed by analyzing the underlying partially accessible queueing system. These lead to the development of two new models for which feasibility is guaranteed. Simulation-based computational experiments show that the proposed models achieve feasibility without significantly increasing the total number of servers. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix of Tables of Computational Results for Section 7.] [ABSTRACT FROM AUTHOR]

Most models for location of immobile congested facilities assume exponentially distributed service time at the facilities. Although the resulting formulations are tractable, they do not adequately represent service time distributions with small variances, as often occur in practice. In a recent paper, the authors utilized an order r Erlang distribution for the service time, applied to the simple case of single-server facilities. We generalize this approach to multiple-server facilities, which need a different mathematical treatment. The constraint on service availability is cast as a linear constraint on the proportion of time the servers are busy, and its righthand side parameter is provided for different situations. Extensive analysis is offered on the influence of the parameters of the service time and the capacity of the facilities on the performance of the system. Numerical results are given for a data set relating to the municipality of Rio de Janeiro. [ABSTRACT FROM AUTHOR]

In telecommunications, packets or units may complete their service in a different order from the one in which they enter the station. In order to reestablish the original order resequencing protocols need to be implemented. In this article, the focus is on a two-server resequencing system with heterogeneous servers and two buffers. One buffer has an infinite capacity to hold the incoming units. The other with a finite capacity is used to resequence the serviced units. This is to maintain the order of departure of the units according to the order of their arrivals. To analyze this resequencing model, we introduce an equivalent two-stage queueing system, namely A. B. Clarke's Tandem Queue, in which the arriving units receive service from only one server, and the units departing from the first stage may be temporally prevented from leaving by occupied service units at the second stage. Our interest is to study the resequencing delay and the sojourn time as times until absorption in suitably defined quasi-birth-and-death processes and continuous-time Markov chains. [ABSTRACT FROM AUTHOR]

The contemporary after-sales market is of increasing importance. One of the features required by the market is to provide differentiated service levels to different groups of customers. We use critical levels as a means to offer differentiation. Critical level policies aim to exploit the differences in target service levels by inventory rationing. In our multi-item single-location spare parts inventory model, we aim to minimize the spare parts provisioning cost, that is inventory holding and transportation cost, under the condition that aggregate mean waiting time constraints for all customer groups are met. In a computational experiment and a case study with data from a company in the semiconductor supplier industry, we show that significant cost reductions can be obtained when critical level policies are used instead of base stock policies (ie policies without critical levels). [ABSTRACT FROM AUTHOR]

Transient solutions for M/M/c queues are important for many purposes, in particular for staffing facilities such as call centers. In this article, we show how to use spectral analysis to find such solutions. The difficulty is that unless the number in line is bounded, one has to deal with matrices of infinite size, and hence with a countable infinite number of eigenvalues. This problem can be overcome by noting that the spectrum is dense with few exceptions. We also show how many discrete eigenvalues remain. Our theory may also work to obtain spectra for other infinite-dimensional matrices. Numerical properties of our approach are explored. [ABSTRACT FROM AUTHOR]

We consider the problem of locating a set of facilities on a network to maximize the expected number of captured demand when customer demands are stochastic and congestion exists at facilities. Customers travel to their closest facility to obtain service. If the facility is full (no more space in the waiting room), they attempt to obtain service from the next-closest facility not yet visited from its current position on the network. A customer is lost either when the closest facility is located too far away or all facilities have been visited. After formulating the model, we propose two heuristic procedures. We combine the heuristics with an iterative calibration scheme to estimate the expected demand rate faced by the facilities: this is required for evaluating objective function values. Extensive computational results are presented. [ABSTRACT FROM AUTHOR]

This paper investigates a discrete-time single-server finite-buffer queueing system with multiple vacations in which arrivals occur according to a discrete-time renewal process. Service and vacation times are mutually independent and geometrically distributed. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer's observation epochs under the late arrival system with delayed access and early arrival system. The analysis of actual waiting-time for both the systems has also been carried out. The model has potential application in high-speed computer network, digital communication systems and other related areas. [ABSTRACT FROM AUTHOR]

This paper describes a decision tool created for the Simcoe County Community Care Access Center (SCCCAC) in Ontario. The tool allows the SCCCAC to quantitatively assess the trade-offs between cost, quality, and waiting time of their home care patients. This information can then be used to negotiate reasonable funding levels with the Ontario government and to appropriately allocate this funding among the various patient groups at the SCCCAC. This work can be expanded to other health care organizations that use prioritized waiting lists. [ABSTRACT FROM AUTHOR]

This paper presents results from a bulk service queueing system, where the main service takes place at fixed time intervals, but where back-up (or relief) services may be introduced in times of heavy demand on the system. On occasions the back-up service itself may receive further back-up services, thus leading to the concept of a cascade of queues flowing from the original main service. Analytic expressions are derived for the mean queue lengths at the points of delivery of service, and the computational requirements are discussed in detail. Sample numerical results and a simple cost analysis are provided. [ABSTRACT FROM AUTHOR]

A new model for call centre queue management is described. It incorporates important features of call centre queues and is shown to produce results that are very different from those produced by the more usual models. The analytic approach is easy to apply, and is used to offer some interesting insights for call center queue management. [ABSTRACT FROM AUTHOR]

When routing dynamically randomly arriving messages, the controller of a high-speed communication network very often gets the information on the congestion state of down stream nodes only after a considerable delay, making that information irrelevant at decision epochs. We consider the situation where jobs arrive according to a Poisson process and must be routed to one of two (parallel) queues with exponential service time distributions (possibly with different means), without knowing the congestion state in one of the queues. However, the (conditional) probability distribution of the state of the unobservable queue can be computed by the router. We derive the joint probability distribution of the congestion states in both queues as a function of the routing policy. This allows us to identify optimal routing schemes for two types of frameworks: global optimization, in which the weighted sum of average queue lengths is minimized, and individual optimization, in which the goal is to minimize the expected delay of individual jobs. [ABSTRACT FROM AUTHOR]

A general model for the description of a discrete-time Markov chain in random environment is introduced. We study the stationary distribution of this model and its relationship with the Palm (embedded) distributions at certain environmental transition epochs. We also study the Events See Time Averages (ESTA) property for this model and we show that it is related to certain partial balance equations and a product-form stationary distribution. Next, we study certain forms of interaction between the environmental process and the process of interest that lead to tractable stationary distributions. More specifically, the stationary distributions of a large class of Markov chains in random environment can be computed efficiently using α-potentials of smaller Markov chains. This decomposability result is also the basis for developing approximations for the stationary distributions of intractable models that evolve in a slowly changing random environment. Moreover, explicit error bounds for these approximations are given. The model can be used for the performance evaluation of discrete time queueing systems in random environment. [ABSTRACT FROM AUTHOR]

Gaussian traffic models are capable of representing a broad variety of correlation structures, ranging from short-range dependent (e.g., Ornstein–Uhlenbeck type) to long-range dependent (e.g., fractional Brownian motion, with Hurst parameter H exceeding ). This note focuses on queues fed by a large number (n) of Gaussian sources, emptied at constant service rate nc. In particular, we consider the probability of exceeding buffer level nb, as a function of b. This probability decaying (asymptotically) exponentially in n, the essential information is contained in the exponential decay rate I(b). The main result of this note describes the duality relation between the shape of I( ⋅ ) and the correlation structure. More specifically, it is shown that the curve I( ⋅ ) is convex at some buffer size b if and only if there are negative correlations on the time scale at which the overflow takes place. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of optimally allocating a sampling budget between the interarrival times and service times for the stationary queue and stationary queue with the goal of minimizing the mean squared error of one of four system performance measures. The natural estimator of the mean waiting time, obtained by substituting estimators for the arrival rate and service rate in the formula for the mean waiting time, has infinite mean squared error and cannot be used. Using an alternative estimator, we propose a two-stage sampling plan and show that this plan is asymptotically risk-efficient in the sense that the mean squared error of the resulting estimator converges to the minimum mean squared error as the sampling budget gets large. Asymptotic normality and other properties of the two-stage estimator are also proved. Simulation results for the system are given to support the theoretical results. **Supported by grant MDA904-00-1-0025 from NSA. [ABSTRACT FROM AUTHOR]