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• A chat service with actively involved customers and repeating interactions is studied. • The capacity of parallel chats and the server's response effort are derived. • A queueing game for a dual-channel system of chat service and call center is analyzed. • Customer bounded rationality is considered. Many service systems in various type of industry provide services via chat technologies. This type of service system is characterized by an interesting combination of properties. First, the customer is actively involved in service execution, since the service is comprised of responses of the server and the customer to each other, until the customer's request is satisfied. In addition, in such a system, the service can be provided by a single server in a parallel manner to a number of customers. Motivated by these and others interesting properties of the chat service, we formulate and analyze the stochastic queueing system as a two-dimensional quasi-birth-and-death process and derive its steady-state probabilities using matrix geometric methods. By means of economic analysis, we provide a scheme for deriving the optimal capacity of parallel chats and the optimal response effort that should be made by the server, considering that higher effort lengthens the response time but increases the probability of successful service completion. We next investigate a queueing game that considers a multi-channel service system consisting of a chat service and a traditional multi-server call center, and we consider strategic customers under both a centralized and a decentralized scenario. We show that competition between service channels may lead to lower service utilization even though customers enjoy higher expected utility. Finally, customer bounded rationality is considered and it is shown that customers who are less rational may enjoy higher utility. Sensitivity analyses are conducted for all scenarios. [ABSTRACT FROM AUTHOR]

Productivity in open pit operations in the mining industry is conditioned by the manual assignment of trucks by the dispatcher, who does not have the ability to find the optimal policy by himself, having many variables that consider. To this end, an MIP optimization model is proposed that considers the scheduling of a discretized operating shift in smaller stages that consider positions and capacities of available trucks, and congestion based on a differential speed based on the number of trucks in different sections of the transport route. The model seeks to prioritize the transfer of material to crushers and meet material goals during the planning horizon. Preliminary results indicate that it is possible to reduce the violation of the production plan by destination by 12% and increase productivity by 46% with respect to the state of the art of similar solutions. [ABSTRACT FROM AUTHOR]

Many infrastructure managers have the goal to increase the capacity of their railway infrastructure due to an increasing demand. While methods for performance calculations of railway line infrastructure are already well established, the determination of railway junction capacity remains a challenge. This work utilizes the concept of queueing theory to develop a method for the capacity calculation of railway junctions, solely depending on their infrastructure layout along with arrival and service rates. The implementation of the introduced approach is based on probabilistic model-checking. It can be used to decide which infrastructure layout to build, i.e. whether an overpass for the analysed railway junction is needed. The developed method addresses the need for fast and reliable timetable-independent railway junction capacity evaluation, catering specifically to the long-term strategic planning of junction infrastructure. • Timetable independent capacity analysis of railway junctions. • Formulation as a queueing system utilizing Continuous-Time Markov Chains. • Application of state-of-the-art probabilistic model-checking to estimate performance indicators. • Decision support for infrastructure managers when planning required infrastructure layouts. • Comparison with classical methods determining the capacity occupation of railway infrastructure. [ABSTRACT FROM AUTHOR]

This paper treats an M/G/1 queue with retrial customers due to server vacation, which can be used to model a hospital service system. When an arriving customer finds the server on vacation at his arrival epoch, he either enters the retrial group with probability p or leaves the system with probability 1 - p. Otherwise, the new arriving customer begins his service immediately if the server is idle upon his arrival or joins the original queue with infinite capacity under FCFS if the sever is busy at his arrival epoch. First, we develop the steady-state analysis by the supplementary variable method and the generating function approach, and give some important performance measures. Moreover, we obtain the Laplace-Stieltjes transform of the sojourn time in the system of an arbitrary customer and prove that the Little's law still holds in our model. Finally, sensitivity analysis and optimal joining policy are given for illustrative purpose. [ABSTRACT FROM AUTHOR]

Highlights • We introduce a spatial queueing link model to consider the effects of spatial queueing and blocking back. • We develop a novel equilibrium model with capacity constraints, queueing delays and blocking back. • The modelling framework is further integrated in a traffic assignment and control problem. • We prove existence of equilibrium results under a variety of scenarios and compare different control policies. • With blocking back, existence of an equilibrium depends on the adopted merge models. Abstract This paper introduces a steady-state, fixed (or inelastic) demand equilibrium model with explicit link-exit capacities, explicit bottleneck or queueing delays and explicit bounds on queue storage capacities. The model is a quasi-dynamic model. The link model at the heart of this quasi-dynamic equilibrium model is a spatial queueing model, which takes account of the space taken up by queues both when there is no blocking back and also when there is blocking back. The paper shows that if this quasi-dynamic model is utilised then for any feasible demand there is an equilibrium solution, provided (i) queue storage capacities are large or (ii) prices are used to help impose capacity restrictions; the prices either remove queueing delays entirely or just reduce spatial queues sufficiently to ensure that blocking back does not occur at equilibrium. Similar results, but now involving the P 0 control policy (introduced in Smith (1979a, 1987)) and two new variations of this policy (i.e., the spatial P 0 control policy, and the biased spatial P 0 control policy) are obtained. In these results, the control policies allow green-times to vary in response to prices as well as spatial queueing delays. These three policies are also tested on a small simple network. In these tests, the biased spatial version of P 0 is much the best in reducing equilibrium delays (on this simple network). The paper further illustrates how the spatial queueing model works on simple networks with different merge models; it is demonstrated that equilibrium may be prevented by certain (fixed ratio) merge models. It is also shown in this case that equilibrium may be imposed on just the controlled area itself by a variety of (merge model, gating strategy) combinations. Opportunities for developing such combined gating and merging control strategies are finally discussed. [ABSTRACT FROM AUTHOR]

Abstract Recently there has been considerable interest in a key paper [1] describing a new approach to congestion control in Internet traffic which has resulted in significant network performance improvement. The approach is based on a 1978 paper [2] and a companion 1979 paper [3] which identified a system operating point that was optimal in that it maximized delivered throughput while minimizing delay and loss. This operating point is simply characterized by the insight that one should "Keep the pipe just full, but no fuller" and we show this is equivalent to loading the system so that in many cases (including those relevant to TCP connections) the optimized average number in the pipe is exactly equal to the Bandwidth-Delay Product. It is important to understand the reasoning and intuition behind this early insight and why it provides such improved behavior of systems and networks. In this paper, we first develop this insight using purely deterministic reasoning. We then extend this reasoning by examining far more complex stochastic queueing systems and networks using a function called Power to mathematically and graphically extract exact and surprising results that support the insight and allow us to identify the optimum operating point for a broad class of systems. These observations allow us to study the impact of Power on networks leading eventually to supporting the statements about steady state congestion and flow control as presented in [1] for today's Internet. We point out that the discussions about the latest congestion control algorithms [ 1 , 4, 5, 6, 7, 8, 9, 10, 11] address the dynamics of tracking flow, dealing with multiple intersecting flows, fairness, and more, and which focus on the dynamic behavior of data networks whereas our work here focuses only on the steady state behavior. [ABSTRACT FROM AUTHOR]

Accidents involving release of chemical, biological, radiological or nuclear substances may prompt the need to decontaminate exposed casualties prior to further medical treatment. Health service workers who carry out decontamination procedures wear protective suits to avoid direct contact with contaminants. We developed an analytical framework based on queueing theory to inform UK Department of Health’s decisions on the stock of protective suits that ambulance services and hospitals with emergency departments in England should hold. Our aim was to ensure that such allocation gave an accepted degree of resilience to locally identified hazards. Here we give an overview of our work and describe how we incorporated information in the public domain about local hazards with expert opinion about the patterns of demand for decontamination associated with different types of incident. We also give an account of how we worked with decision makers to inform national guidance on this topic. [ABSTRACT FROM AUTHOR]

Service systems often experience time-dependent aspects, typically due to time-dependent arrivals and capacities. Easy and quick to use queueing expressions generally do not apply to these situations, but are still used. At the same time a large number of computational papers exist that deal with queue length distributions for time-dependent queues. Most of these are fairly theoretical and based on single queues. Real-life service systems, however, might resemble a queueing network structure. With this paper we aim to bring both worlds together. It presents a computational method for time-dependent queueing networks based on uniformization. Although uniformization is generally perceived to be too computationally prohibitive, we show that our method is very effective for practical instances, as shown with a Dutch blood collection site. The results shown in this paper take a matter of seconds to compute. The objective of the results is twofold: (1) to show that the time-dependent queueing network approach is imperative for some queueing networks, including this application and (2) to evaluate possible improvement scenarios for Dutch blood collection sites that can only be properly assessed with a time-dependent queueing method. [ABSTRACT FROM AUTHOR]

Analysis of an unreliable-server retrial queue with customer's feedback and impatience is presented. Truncated classical and constant retrial policies are taken into account. This system is analyzed as a process of quasi-birth-and-death (QBD). The quasi-progression algorithm is applied to compute the rate matrix of QBD model. A recursive solver algorithm for computing the stationary probabilities is also developed. To make the investigated system viable economically, a cost function is developed to decide the optimum values of servers, mean service rate and mean repair rate. Quasi-Newton method, pattern search method and Nelder–Mead simplex direct search method are employed to implement the optimization tasks. Under optimum operating conditions, numerical results are provided for a comparison of retrial policies. We also give a potential application to illustrate the system's applicability. [ABSTRACT FROM AUTHOR]

• A simple example network is considered, with a merge and a downstream bottleneck. • Upstream gating is imposed at the merge to reduce the queue at the downstream bottleneck. • It is shown that using flows to control the upstream merge does not maximise network capacity. • It is shown that using delays to control the upstream merge does maximise network capacity. This paper considers a simple network with a merge and a downstream bottleneck, which corresponds to a very congested part of the City of York road network - Gillygate. We focus on "upstream-gating" control strategies which hold traffic back at traffic signals just ahead of the merge to prevent the formation of a queue at a downstream bottleneck; and we also consider different ways of further, additionally, controlling the two inflows to the merge. We show, by considering the simple network, that if the added upstream merge-control uses only flows to control the two approaches to the merge then equilibrium may not exist. For example, with the "zipper" rule (which equalises the two inflows at the merge) an equilibrium cannot exist for certain feasible demands on this network. On the other hand, we show that adding upstream merge-control which equalises the two delays felt at the merge allows an equilibrium for all feasible demands on this network, and so maximises the network capacity, notwithstanding the upstream gating. This suggests that, in general, delays should probably be used to control merges and downstream queues, rather than only flows, if network capacity is to be maximised. This observation may help the design of good control strategies, using both flows and delays, for upstream-gating designed to remove or reduce queues at specific downstream locations. The equilibrium analysis in our example is supported by (i) a dynamic analysis allowing for the dynamic growth of queues in the example network and (ii) real-life results of upstream-gating applied to Gillygate in York (UK) which provided motivation for this paper. The analysis here makes reasonable allowance for the spatial extent of queues but does not consider within-cycle or cycle-to-cycle queueing dynamics. [ABSTRACT FROM AUTHOR]

For a given Lévy process X = ( X t ) t ∈ R + and for fixed s ∈ R + ∪ { ∞ } and t ∈ R + we analyse the future drawdown extremes that are defined as follows: D ¯ t , s ∗ = sup 0 ≤ u ≤ t inf u ≤ w < t + s ( X w − X u ) , D ¯ t , s ∗ = inf 0 ≤ u ≤ t inf u ≤ w < t + s ( X w − X u ) . The path-functionals D ¯ t , s ∗ and D ¯ t , s ∗ are of interest in various areas of application, including financial mathematics and queueing theory. In the case that X has a strictly positive mean, we find the exact asymptotic decay as x → ∞ of the tail probabilities P ( D ¯ t ∗ < x ) and P ( D ¯ t ∗ < x ) of D ¯ t ∗ = lim s → ∞ D ¯ t , s ∗ and D ¯ t ∗ = lim s → ∞ D ¯ t , s ∗ both when the jumps satisfy the Cramér assumption and in a heavy-tailed case. Furthermore, in the case that the jumps of the Lévy process X are of single sign and X is not subordinator, we identify the one-dimensional distributions in terms of the scale function of X . By way of example, we derive explicit results for the Black–Scholes–Samuelson model. [ABSTRACT FROM AUTHOR]

A queueing model with catastrophes and delayed action is studied in this paper. This delayed action could be in the form of protecting or removing all the customers that are in the system based on the outcome of two random clocks which are simultaneously activated upon the occurrence of a catastrophic event. Assuming the customers to arrive according to a versatile Markovian point process to a single server system, the service times to be of phase type, and all other underlying random variables to be exponentially distributed, we use matrix-analytic methods to study the delayed catastrophic model in steady-state. Needed expressions for the number in the system as well as the waiting time distributions are derived along with a discussion on some special cases of this model. Detailed illustrative examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we present a comparative study on the total revenue generated with pre-emptive and non pre-emptive priority scheduler for a fairly generic problem of pricing the server’s surplus capacity in a single server Markovian queue. The specific problem is to optimally price the server’s surplus capacity by introducing a new class of customers (secondary class) without affecting the pre-specified service level of its current customers (primary class) when pre-emption is allowed. Pre-emptive scheduling is used in various applications. First, a finite step algorithm is proposed to obtain global optimal operating and pricing parameters for this problem. These optimal operating and pricing parameters constitute a unique Nash equilibrium in a certain two player non cooperative game. We then describe the range of service level where pre-emptive scheduling gives feasible solution and generates some revenue while non pre-emptive scheduling has infeasible solution. Further, some complementary conditions are identified to compare revenue analytically for certain range of service level where strict priority to secondary class is optimal. Our computational examples show that the complementary conditions adjust in such a way that pre-emptive scheduling always generates more revenue. Theoretical analysis is found to be intractable for the range of service level when pure dynamic policy is optimal. Hence, extensive numerical examples are presented to describe different instances. It is noted in numerical examples that pre-emptive scheduling generates at least as much revenue as non pre-emptive scheduling. A certain range of service level is identified where improvement in revenue is quite significant. [ABSTRACT FROM AUTHOR]

We investigate the staffing problem at Peace Arch, one of the major U.S.–Canada border crossings, with the goal of reducing time delay without compromising the effectiveness of security screening. Our data analytics show how the arrival rates of vehicles vary by time of day and day of week, and that the service rate per booth varies considerably by the time of day and the number of active booths. We propose a time-varying queueing model to capture these dynamics and use empirical data to estimate the model parameters using a multiple linear regression. We then formulate the staffing task as an integer programming problem and derive a near-optimal workforce schedule. Simulations reveal that our proposed workforce policy improves on the existing schedule by about 18% in terms of average delay without increasing the total work hours of the border staff. [ABSTRACT FROM AUTHOR]

The operation of railway systems requires detailed information on infrastructure capacity. A major challenge, especially in long-term planning, is assessing the quality of operations given very limited information on schedules is available. To this end, analytical models based on a stochastic description of railway systems have found widespread application. We discuss a model for the capacity analysis of railway lines relying on single channel queueing systems. By identifying knock-on delays with waiting times delays can be estimated using methods from stochastics and queueing theory. Mean knock-on delays are used as a quality-dependent indicator of capacity allowing to determine the admissible number of trains for a prescribed level of service. Though being widely used in Germany the model has not been made fully available to the research community. In this paper two main contributions are made: A new, mathematically rigorous derivation of the pivotal “Strele Formula” for the estimation of knock-on delays, which is based on the convolution of delay distribution functions, is provided. Unlike existing discussions our approach is valid for general independent buffer times. Additionally, we critically review the model assumptions and investigate the “triangular gap problem”, an overestimation of capacity resulting from the model’s limitation to pairwise correlations. [ABSTRACT FROM AUTHOR]

In recent decades, discrete event simulation (DES) has been widely used for analyzing construction projects. Recently, fuzzy discrete event simulation (FDES), which is an integration of fuzzy set theory with DES, has been proposed for simulating construction projects. FDES provides a framework to consider subjective uncertainty (uncertainty due to vagueness, subjectivity, and linguistic expression of knowledge) in construction simulation models. Current FDES frameworks only calculate simulation time (e.g., project completion time) as the simulation output. However, queue performance measures (e.g., average queue length and waiting time)—though important simulation model outputs for decision making, finding bottlenecks, and optimizing construction resources—are not analyzed in current FDES methodologies. Using fuzzy logic to consider the subjective uncertainty of service time and the inter-arrival time of systems' queues may improve such simulation models by more realistically representing their results. This paper provides a novel methodology to consider subjective uncertainty in analyzing the fuzzy queues in construction FDES models. Incorporating fuzzy queuing theory with FDES methodology as proposed in this paper enhances the applicability of FDES in construction projects. The proposed methodology is validated through mathematically solved queueing examples, and its practical aspects are illustrated using an example of an asphalt paving operation. [ABSTRACT FROM AUTHOR]

As blood donations are provided on a voluntary non-remunerated basis, blood donors should be treated as user-friendly as possible. Delays and waiting times within blood collection sites (donor centers) should thus be kept at acceptable levels. Waiting times are not incorporated directly other than by practical experience. A more rigorous approach is required. An analytic waiting time computation is therefore investigated to compute waiting times as a function of production. An analytic so-called product form solution for joint queue lengths is concluded. This product form leads to: • an exact expression for the marginal waiting time percentiles at each separate phase • a more formal justification for approximate computation of the total mean waiting time for the non-exponential case. A computational algorithm is provided to numerically approximate the total delay time distribution, an algorithm that has not been presented before. The results are tested for and applied to a real life test case of a Dutch representative blood collection site. These results illustrate the practical usefulness for Sanquin, but also the applicability of the models in general. [ABSTRACT FROM AUTHOR]

Let τ ( x ) be the epoch of first entry into the interval ( x , ∞ ) , x > 0 , of the reflected process Y of a Lévy process X , and define the overshoot Z ( x ) = Y ( τ ( x ) ) − x and undershoot z ( x ) = x − Y ( τ ( x ) − ) of Y at the first-passage time over the level x . In this paper we establish, separately under the Cramér and positive drift assumptions, the existence of the weak limit of ( z ( x ) , Z ( x ) ) as x tends to infinity and provide explicit formulas for their joint CDFs in terms of the Lévy measure of X and the renewal measure of the dual of X . Furthermore we identify explicit stochastic representations for the limit laws. We apply our results to analyse the behaviour of the classical M/G/1 queueing system at buffer-overflow, both in a stable and unstable case. [ABSTRACT FROM AUTHOR]

• The congested facility location problem with unreliable servers is modeled. • Queueing models with interruptions are used to analyze servers' status. • A problem-based B&B algorithm is designed to solve the problem exactly. • The B&B algorithm outperforms the BARON solver in solving different size instances. • The antlion optimization algorithm is proposed to solve large-sized problems. This research addresses the location problem of congested facilities, assuming service interruptions and customer withdrawals. Service interruptions can occur as a result of events such as machine failures, power outages, and communication system disconnections. As long as no interruption occurs, each facility functions as a M/M/1 queuing system. Upon an interruption, the server stops working, and customers receiving service or waiting in line leave the queue before being served. Moreover, customers who visit the facility during the repair avoid entering the facility. The problem is first formulated as a mixed-integer nonlinear programming (MINLP) model, for which two piecewise mixed-integer linear programming (MILP) relaxations, an exact solution algorithm (the branch and bound algorithm), and a metaheuristic algorithm (the antlion algorithm), are then presented for solution. Numerical experiments indicate the efficiency of the branch and bound algorithm. The antlion algorithm also exhibits the proper convergence speed to obtain near-optimal solutions. [ABSTRACT FROM AUTHOR]

Abstract: Economou and Kanta (2008) [4] considered equilibrium customer strategies in the observable M/M/1 queue with an unreliable server. It is assumed that the server alternates between on and off periods. Upon arrival, the customers can observe the queue length and will decide whether to join or balk the system according to the information about the server’s state based on a linear reward-cost structure. In this paper, the corresponding unobservable cases in which the queue length is unobservable to arriving customers are investigated. The mixed equilibrium balking strategies are derived in two cases, according to the information on the server’s state. Numerical examples are presented to illustrate the effect of the information levels on the behavior of the customers. [Copyright &y& Elsevier]

Abstract: Hospital waiting times are considerably long, with no signs of reducing any-time soon. A number of factors including population growth, the ageing population and a lack of new infrastructure are expected to further exacerbate waiting times in the near future. In this work, we show how healthcare services can be modelled as queueing nodes, together with healthcare service workflows, such that these workflows can be optimised during execution in order to reduce patient waiting times. Services such as X-ray, computer tomography, and magnetic resonance imaging often form queues, thus, by taking into account the waiting times of each service, the workflow can be re-orchestrated and optimised. Experimental results indicate average waiting time reductions are achievable by optimising workflows using dynamic re-orchestration. [Copyright &y& Elsevier]

Abstract: In this paper we study a queueing model in which the customers arrive according to a Markovian arrival process (MAP). There is a single server who offers services on a first-come-first-served basis. With a certain probability a customer may require an optional secondary service. The secondary service is provided by the same server either immediately (if no one is waiting to receive service in the first stage) or waits until the number waiting for such services hits a pre-determined threshold. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples are discussed. [Copyright &y& Elsevier]

Abstract: The equilibrium balking strategies are investigated in the paper for observable and unobservable single-server queues with working vacations. In such an M/M/1 queue with working vacations, the server undertakes the workload with a lower service rate rather than completely stops to work during the vacation period. Upon arrival, the customers decide whether to join or balk the queue based on observation of the queue length and the status of the server, along with the reward-cost structure of the system. Accordingly, four cases with respect to different levels of information are studied and the corresponding Nash equilibria are derived. Finally, the effect of the information levels as well as several parameters on the equilibrium threshold and equilibrium entrance probabilities is illustrated by numerical examples. [Copyright &y& Elsevier]

Abstract: A link-based elastic demand equilibrium model with explicit link-exit capacities and explicit bottleneck or queuing delays is specified. The model, which is at the borderline between steady state and dynamic equilibrium transport models, may be used to compare different proposed short run ITS strategies (using small or even zero elasticity) and also different proposed long term strategies (using greater elasticity); increasing the consistency between short and long run model evaluations. It is shown that, under very weak conditions, there is a solution to the model. A solution algorithm is suggested and a proof of convergence, under natural conditions, is provided. The model is based on link rather than route flows; so it is suitable for large networks as well as small networks. [Copyright &y& Elsevier]

Abstract: In this paper, a dynamic nearest neighbor (DNN) policy is proposed for operating a fleet of vehicles to serve customers, who place calls in a Euclidean service area according to a Poisson process. Each vehicle serves one customer at a time, who has a distinct origin and destination independently and uniformly distributed within the service area. The new DNN policy is a refined version of the nearest neighbor (NN) policy that is well known to perform sub-optimally when the frequency of customer requests is high. The DNN policy maintains geographically closest customer-to-vehicle assignments, due to its ability to divert/re-assign vehicles that may be already en-route to pick up other customers, when another vehicle becomes available or a new customer call arrives. Two other pertinent issues addressed include: the pro-active deployment of the vehicles by anticipating in which regions of the service area future calls are more likely to arise; and, imposition of limits to avoid prohibitively long customer wait times. The paper also presents accurate approximations for all the policies compared. Extensive simulations, some of which are included herein, clearly show the DNN policy to be tangibly superior to the first-come-first-served (FCFS) and NN policies. [Copyright &y& Elsevier]

Abstract: Although a large number of different methods for establishing the fitting parameters of PH distributions to data traces (PH fitting) have been developed, most of these approaches lack efficiency and numerical stability. In the present paper, a restricted class of PH distribution, called the hyper-Erlang distribution (HErD), is used to establish a maximum likelihood estimation model for data tracing. To fit the parameters, a hybrid algorithm based on the scatter search algorithm, the improved adaptive genetic algorithm, and the expectation maximization algorithm was developed to obtain the SS&IAGA-EM algorithm, which has a polynomial time complexity. In the data tracing tests for different distribution functions, the results obtained from SS&IAGA-EM and from the G-FIT, which is currently the best software for PH fitting, were compared. The present paper demonstrates that (a) the fitting effect of G-FIT does not positively correlate with the number of states of a HErD; thus, G-FIT repeatedly has to test the number of states manually to achieve a satisfactory fitting effect; (b) although setting range of the number of branches in G-FIT could mitigate the aforementioned deficiency, the combinations of the number of phases per branch grow exponentially; and (c) on SS&IAGA-EM can optimize the number of states and the number of phases automatically, aside from being slightly faster than G-FIT for a small number of branches and is significantly faster for a large number of branches. Moreover, in all tests, SS&IAGA-EM can achieve the same fitting quality as G-FIT for the same number of states. [Copyright &y& Elsevier]

Abstract: We consider a multi-server queueing system in which two types of customers arrive according to a Markovian arrival process. Type 1 customers have preemptive priority over Type 2 customers. A Type 2 arrival finding all servers busy will be lost. However, a Type 1 customer finding all servers busy with at least one Type 2 in service will get into service by pre-empting one of the Type 2 customers in service. Pre-empted Type 2 customers enter into a buffer of finite capacity. These (preempted) customers eventually leave the system after completing a service. In the case of exponential services, this model is studied analytically in steady-state by exploiting the special nature of the queueing model. A number of useful performance measures along with some illustrative examples are reported. In the case of non-exponential services, we simulate the model and discuss the effect of the variatio the services on some selected performance measures. [Copyright &y& Elsevier]

Abstract: Several recent papers have investigated the customer reneging behavior in queueing systems with vacations, where the customers become impatient during the absence of the server(s). These studies have treated the cases of independent and synchronized abandonments. In the case of independent abandonments, the customers have their own independent patience times and abandon the system when such times expire. In the case of synchronized abandonments, the abandonment opportunities occur according to a certain point process and then all present customers decide simultaneously but independently whether they will abandon the system or not. In the present paper, we complement these studies by considering the case of geometric abandonments. This case arises when the abandonment opportunities occur according to a certain point process and the customers decide sequentially whether they will leave the system or not. We derive explicit expressions and computational schemes for various performance descriptors, including the number of customers in system, the sojourn time of a customer, the duration and the maximum number of customers in a busy period. [Copyright &y& Elsevier]

Abstract: The blocking probability is commonly used to evaluate the quality-of-service (QoS) offered by dialup Internet Service Providers (ISPs). Unfortunately, dialup ISPs employ no blocking standards or thresholds. This raises questions as to exactly how providers measure and evaluate QoS with respect to network access and how they make capacity planning decisions. Many ISPs use the User-to-Modem Ratio (UMR) as a surrogate measure for service quality, but there are no well defined direct relationships between the UMR and the blocking probability. In this paper, relationships between the UMR and other well known traffic variables and the blocking probability are quantified, and the usefulness of the UMR as a standalone QoS metric is explored. Blocking probabilities are estimated for a range of UMRs via simulation from a range of demand scenarios developed from observed data. A predictive regression model is introduced to quantify the affects of independent predictor variables on blocking. Results show that the UMR is not a useful standalone QoS metric and traditionally favored UMRs such as 10:1 cannot be associated with “high quality service” in a de facto manner. [Copyright &y& Elsevier]

Abstract: This paper presents a functional approximation of the M/D/1/N built on a Taylor series approximation. Numerical examples are carried out to illustrate the performance of our approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper suggests that introducing randomization in queue discipline might be welfare enhancing in certain queues for which the cost of waiting is a concave function of waiting time. Concavity can make increased variability in waiting times good not bad for aggregate customer welfare. Such concavity may occur if the costs of waiting asymptotically approach some maximum or if the customer incurs a fixed cost if there is any wait at all. As examples, cost might asymptotically approach a maximum for patients seeking organ transplants who will not live beyond a certain threshold time, and fixed costs could pertain for knowledge workers seeking a piece of information that is required to proceed with their current task, so any delay creates a “set up charge” associated with switching tasks. [Copyright &y& Elsevier]

Abstract: We consider a single server queueing system in which arrivals occur according to a Markovian arrival process. The system is subject to disastrous failures at which times all customers in the system are lost. Arrivals occurring during the time the system undergoes repair are stored in a buffer of finite capacity. These customers can become impatient after waiting a random amount of time and leave the system. However, these customers do not become impatient once the system becomes operable. When the system is operable, there is no limit on the number of customers who can be admitted. The structure of this queueing model is of -type that has been extensively studied by Neuts and others. The model is analyzed in steady state by exploiting the special nature of this type queueing model. A number of useful performance measures along with some illustrative examples are reported. [Copyright &y& Elsevier]

Abstract: In this paper, we study the effects of considering homogeneous versus non-homogeneous servers in applications of the hypercube queueing model. This is important since approximate methods available for solving the model for homogeneous servers are computationally much less time-consuming than the exact methods required for the non-homogeneous case. Illustrative examples are initially presented to show the degree to which using homogeneous versus non-homogeneous servers can differ. Then, two ambulance deployment applications dealing with Brazilian emergency medical systems, in a city and along a highway, are analyzed. The basic operational characteristics of non-homogeneous systems were compared to the respective predictions produced under the simplifying assumption of homogeneous servers. It was found that, even when the degree of non-homogeneity of the servers is not highly significant, homogeneity may lead to poor predictions of the actual operational characteristics of non-homogeneous systems. [Copyright &y& Elsevier]

Abstract: This article deals with a hybrid system, in which a single server processes two different queues of units, one called primary and the other one — secondary. The queueing process in the primary system is formed by a Poisson flow of groups of units, while the secondary system is closed. The server’s primary appointment (in hybrid mode I) is to process units in batches until the buffer content drops significantly. In this case, the server takes over a queue in the secondary system (activating hybrid mode II), and he is to complete some minimum amount of jobs (rendered in groups of random sizes during random times). When he is done with this work, he returns to the primary system. If the queue there is not long enough, he waits, thereby activating hybrid mode III. The authors first apply and embellish some techniques from fluctuation theory to find the exit times from respective hybrid modes and queue levels in both systems in terms of their joint functionals. The results are then utilized for the subsequent (semi-regenerative) analysis of the evolution of queueing processes. The authors obtain explicit formulas for the limiting distribution of the queueing process and the mean number of units processed in the secondary system. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a two-class single-server preemptive priority queueing system with arrivals to each class are assumed to follow a Poisson process with exponentially distributed service times. Customers are served on a first-come, first-served basis within their own queue. Explicit expressions for the mean queue length and the steady-state joint distribution of the number of high and low priority customers in the system are derived. The analysis is based on the generating function technique. The obtained expressions are free from Bessel functions or any integral functions. Moreover, numerical values testing the quality of our analytical results are also presented. [Copyright &y& Elsevier]

Abstract: We consider the problem of determining the initial spare inventory level for a multi-echelon repairable item inventory system. We extend the previous results to the system, which has an inventory at the central depot as well as at bases and with a general repair time distribution. We propose an algorithm which finds spare inventory level to minimize the total expected cost and simultaneously to satisfy a specified minimum service rate. Extensive computational experiments show that the algorithm is accurate and efficient. [Copyright &y& Elsevier]

Abstract: The paper presents an approach predicting the scheduled waiting time by means of a semi-Markovian queueing model. For that, the process of timetable compilation in a railway network with open access is shortly explained and described by means of queueing theory. The arrival process is determined by the requested train-paths. The description of the service process is based on an application of the theory of blocking times and minimum headway times. The approach is useful for predicting a quality measure for bottlenecks with mainly non-cyclic timetable structures. [Copyright &y& Elsevier]

Abstract: We consider a multi-server retrial queueing model in which arrivals occur according to a Markovian arrival process. Using continuous-time Markov chain with absorbing states, we determine the distribution of the maximum number of customers in a retrial orbit. Illustrative numerical examples that reveal some interesting results are presented. [Copyright &y& Elsevier]

Abstract: This article analyzes a stochastic hybrid system with compound Poisson input, general batch service, and two vacation modes that operate in accordance with a so-called “bilevel hysteretic control.” In the context of queues with vacations, most stochastic systems function either under multiple or single vacation regimes and they are initiated whenever the queue length becomes zero. In this model we combine the two modes in one hybrid system that switches to a multiple or single vacation modes (which consists of multiple or single segments), respectively, whenever the queue drops below some or falls into upon the end of a service. The servicing facility then assumes some other activities. The main service is restored when the queue length reaches or exceeds some upon the completion of a vacation segment. We use fluctuation analysis and semi-regenerative techniques to arrive at closed form functionals for the steady state probabilities of queueing processes both for discrete and for continuous time parameter processes and discuss special cases to demonstrate the applicability of the results. The latter can potentially be used to optimize the system with respect to parameters and . [Copyright &y& Elsevier]

Abstract: In this paper, I propose a new methodology to find the bicriteria shortest path from the source to the sink node of a network of queues under the steady-state condition. I assume the number of servers in each service station settled in a node of the network is either one or infinity. Moreover, the arc lengths are mutually independent random variables. First, I propose a method to transform each node, containing a service station, into a proper stochastic arc corresponding to the waiting time in the particular service station. Then, the stochastic network is transformed into a bicriteria network by computing the mean and the variance of the waiting time in each service station and augmenting those to the transformed arc. Finally, by defining a proper utility function, dynamic programming is used to obtain the bicriteria shortest path. The time complexity of the proposed algorithm is O(b), considering b as the number of service stations. The proposed method is suitable to find the shortest rout from the origin to the destination in stochastic routing problems. Moreover, this method is useful to approximate the mean and the variance of project completion time in dynamic PERT networks. [Copyright &y& Elsevier]

Abstract: The paper considers a dynamic traffic assignment model with deterministic queueing and inelastic demand for each origin–destination (OD) pair in the network. Two types of time-varying behaviour are modelled. First, within-day time is regarded as a continuous variable. During each day, flows propagating through routes connecting OD pairs are represented by non-negative, essentially bounded and measurable functions. Also, day-to-day time is (slightly surprisingly) modelled as if it were continuous. The day-to-day dynamical system that is adopted is derived naturally from the usual user equilibrium condition. The route cost is shown to be a Lipschitz continuous function of route flow in the single bottleneck per route case. Global convergence to equilibrium is shown to be guaranteed when the route cost vector is a non-decreasing (monotone) function of the route flow vector. In the single bottleneck per route case, the route cost function is shown to be a monotone function of the route flow if the bottleneck capacities are all non-decreasing as functions of within-day time. Monotonicity of the route cost function is also shown to hold when each bottleneck has at most one route passing through it. [Copyright &y& Elsevier]

Abstract: We develop a multi-objective model for the resource allocation problem in a dynamic PERT network, where the activity durations are exponentially distributed random variables and the new projects are generated according to a Poisson process. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a Poisson process with the generation rate of new projects. It is assumed that the mean time spent in each service station is a non-increasing function and the direct cost of each activity is a non-decreasing function of the amount of resource allocated to it. The decision variables of the model are the allocated resource quantities. To evaluate the distribution function of total duration for any particular project, we apply a longest path technique in networks of queues. Then, the problem is formulated as a multi-objective optimal control problem that involves three conflicting objective functions. The objective functions are the project direct cost (to be minimized), the mean of the project completion time (min) and the variance of the project completion time (min). Finally, the goal attainment method is applied to solve a discrete-time approximation of the original optimal control problem. We also computationally investigate the trade-off between accuracy and the computational time of the discrete-time approximation technique. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a multi-objective model to optimally control the lead time of a multistage assembly system, using an interactive method. The multistage assembly system is modelled as an open queueing network, whose service stations represent manufacturing or assembly operations. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite number of servers (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The transport times between the service stations are independent random variables with generalized Erlang distributions. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), the variance of the lead time (min) and the probability that the manufacturing lead time does not exceed a certain threshold (max). Finally, the STEM method is used to solve a discrete-time approximation of the original problem. We also investigate the trade-off between the accuracy (correctness) and the computational time of the proposed approximation technique. [Copyright &y& Elsevier]

Abstract: An i.i.d. process is considered on a compact metric space . Its marginal distribution is unknown, but is assumed to lie in a moment class of the form, where are real-valued, continuous functions on , and are constants. The following conclusions are obtained: [(i)] For any probability distribution on , Sanov’s rate-function for the empirical distributions of is equal to the Kullback–Leibler divergence . The worst-case rate-function is identified as where , and is a compact, convex set. [(ii)] A stochastic approximation algorithm for computing is introduced based on samples of the process . [(iii)] A solution to the worst-case one-dimensional large-deviation problem is obtained through properties of extremal distributions, generalizing Markov’s canonical distributions. [(iv)] Applications to robust hypothesis testing and to the theory of buffer overflows in queues are also developed. [Copyright &y& Elsevier]

Abstract: We study a single server queueing system whose arrival stream is compound Poisson and service times are generally distributed. Three types of idle period are considered: threshold, multiple vacations, and single vacation. For each model, we assume after the idle period, the server needs a random amount of setup time before serving. We obtain the steady-state distributions of system size and waiting time and expected values of the cycle for each model. We also show that the distributions of system size and waiting time of each model are decomposed into two parts, whose interpretations are provided. As for the threshold model, we propose a method to find the optimal value of threshold to minimize the total expected operating cost. [Copyright &y& Elsevier]