Search

Some discrepancies in an earlier paper describing a bulk service queuing situation with customer balking or reneging are pointed out. Necessary modifications to make the model more valid are incorporated in a reformulation and an approach for developing the state-time probabilities of the system is suggested. [ABSTRACT FROM AUTHOR]

This paper discusses the following model: (i) Arriving customers are accepted in the system in a time interval [t[sub0], t'] and are rejected with compensation after time t'; (ii) the server runs at the cost rate r[sub0] in a time interval [t[sub0], T], t[sub0]≤t' ≤ T, and runs at the increased cost rate r[sub1](r[sub1] > r[sub0]) after the closing time T, until the system becomes empty after time t'. The time t' is called the rejection time. The paper finds the optimal rejection time, that is, the rejection time that minimizes the expected total cost. It can be shown that in certain cases the optimal rejection time can be determined by a nonlinear equation. Numerical examples are given for an M/M/1 queuing system, and the more generalized model is briefly discussed. [ABSTRACT FROM AUTHOR]

This paper provides the solution to the problem of the distribution of busy periods of the single-channel queue characterized by a time-dependent Poisson-distributed arrival rate and a general class of holding times. The notation is chosen in such a fashion that the main body of computations and mathematical analysis is identical with what was required in the solution of the general queuing equations considered in a previous paper which should be read first [4]. The solution of the problem for winch the traffic intensity is constant and the holding time distribution is Pearson type III is derived in closed form in terms of the Ink functions introduced previously. [ABSTRACT FROM AUTHOR]

In this paper the authors study the queues that build up in a minor stream of traffic waiting to cross or merge with a major stream The criterion for joining or crossing is that a gap between veincles in the major stream be greater than or equal to some constant value Several authors have studied the case where bulk service is provided for the minor stream queue with the appearance of each gap, in this paper the authors emphasize the higher flow rate situations where one car in the minor stream queue is released in a first-come first-serve fashinon with the appearance of a gap It is assumed that the minor stream is Poisson-fed while the intervehicle headways inq the major stream are arbitrary but identically and independently distributed random variables. [ABSTRACT FROM AUTHOR]

In this paper we investigate the output process of the M/D/1 queuing system. We derive expressions for the distributions and first two moments, in both steady-state and transient conditions, of the following random variables: (1) the time until the nth departure measured from a departure epoch, To, (2) the time between the n--1st and nth departures after To, and (3) the number of departures in (T[sub 0], T[sub 0]+t]. Further we study the autocorrelation functions of random variables (1) and (2) in the steady state. [ABSTRACT FROM AUTHOR]

Using the technique employed by the author in an earlier paper, the existence of an optimal stationary policy that can be obtained from the usual functional equation is again established in the presence of a bound (not necessarily polynomial) on the one-period reward of a semi-Markov decision process. This is done for both the discounted and the average cost case. In addition to allowing an uncountable state space, the law of motion of the system is rather general in that we permit any state to be reached in a single transition. There is, however, a bound on a weighted moment of the next state reached. Finally, we indicate the applicability of these results. [ABSTRACT FROM AUTHOR]

This paper considers a preemptive priority and a nonpreemptive priority queuing model in the steady state. Each model assumes two priority levels, a single-service channel, no queue-length limit, and negative exponential interarrival-time and service-time distributions. The paper develops a set of computationally efficient recursion formulas that allow exact calculation of the state probabilities. In the nonpreemptive-priority case, this is the first time that a complete solution for the equilibrium-state probabilities has been obtained. [ABSTRACT FROM AUTHOR]

This paper presents results in the ergodic theory of Markov chains that are useful in certain cases where the well known theory d Form and PAlm is not applicable. The paper gives the background leading to the results describes their significance, proves two theorems, and presents an example. The conditions for ergodicity are based on the notion of conditional single transition displacement of a Markov chain due to Pakes. [ABSTRACT FROM AUTHOR]

In this paper Kendall's technique of the embedded Markov chain[5] is applied to a queuing system `with general independent input and a wide class of service-time distributions The matrix of transition probabilities is found to be formally identical `with that discussed in our earlier study,[9] which will be taken as read in the present paper Using the results of reference 9 we can write down the equilibrium distribution of waiting-times for customers in the more general system in terms of the roots of a transcendental equation An example is considered that arose in Bailey's study of hospital systems[1] [ABSTRACT FROM AUTHOR]

This article presents a comment on the article "A queuing Model for Unitized Cargo Generation," by A. Novaes and E. Frankel, published in the January-February, 1966 issue of the journal "Operations Research." It describes a model in which customers balk with a probability depending on a function of the queue size. This note attempts to rectify the inaccuracies of their article. The same notation as theirs is adopted here to ease recognition of the differences.

Presents several letters to the editor commenting on issues related to distribution theory of economics. Comments on the article "The Remaining Busy Period for a Single Server Queue With Poisson Input;" Discussion on non-optimality of planned replacement in intervals of decreasing failure rate; Assumptions on a known failure distribution F(t) with failure rate q(t).

Presents a letter to the in response to the article on the least positive root of an equation in queueing theory.

This paper considers a special queue situation, one in which a single facility serves two major priority classes of customers. Within each class, there are several levels of priorities. The first class has the higher priority. On arrival, a customer of the first class immediately replaces any customer of lower priority being sewed. The second class has the lower priority, as compared to the first class. On its arrival, a customer of the second class cannot interrupt the current service of a lower priority customer in the system; it must wait until the service is completed. The first class is the preemptive priority, and the second class is the nonpreemptive priority. This paper formulates a theoretical solution for this queuing system, which has a wide range of application in the computer industry. The real-time control program under the multiprogramming environment is an analog of this priority queuing model. [ABSTRACT FROM AUTHOR]

This note gives a rigorous proof of the queuing formula L=λW, using as hypotheses only that the limiting averages, λ and W, exist and are finite. The proof is related to one given in a previous paper by the author that used a discounted analogue and Tauberian theorems. The proof in the present paper, however, is direct and avoids the use of transforms. Some comments are offered on the relation between the proof and the heuristic arguments for L= λW commonly encountered in the literature. [ABSTRACT FROM AUTHOR]

The previous papers in this series developed a methodology for obtaining from certain simulations confidence intervals for parameters associated with the steady-state distribution. This methodology required the simulations to contain an embedded renewal process at whose epochs the simulation started from scratch. The present paper contains four approximation techniques for obtaining confidence intervals when the simulation does not contain the required renewal process. [ABSTRACT FROM AUTHOR]

The D-policy is defined as a control policy which turns the server on when the total work to be done reaches the value D. This paper corrects the expression derived in an earlier paper for the expected cost per unit time. Consequently, the D-policy is shown to be superior to the Heyman, Yadin-Naor N-policy (which turns the server on when the queue size reaches the value N) for the service time distributions distributed as exponential, with decreasing failure rates and for some cases with increasing failure rates. [ABSTRACT FROM AUTHOR]

This paper relates to a queueing system with Poisson input and exponential service time, service taking place in batches under a 'general bulk service rule'. (A batch will contain no fewer than 'a' and no more than 'b' units.) The object of this paper is to study the waiting time distribution of such a bulk service system under steady state and also to indicate how the moments of the distribution can be obtained. [ABSTRACT FROM AUTHOR]

This paper considers a special queue situation, one in which a single facility serves two major priority classes of customers. Within each class, there are several levels of priorities. The first class has the higher priority. On arrival, a customer of the first class immediately replaces any customer of lower priority being served. The second class has the lower priority, as compared to the first class. On its arrival, a customer of the second class cannot interrupt the current service of a lower priority customer in the system; it must wait until the service is completed. The first class is the preemptive priority, and the second class is the nonpreemptive priority. This paper formulates a theoretical solution for this queuing system, which !urn a wide range of application in the computer industry. The real-time control program under the multiprogramming environment is an analog of this priority queuing model. [ABSTRACT FROM AUTHOR]

Queueing Theory has been attacked on two fronts. Some theoreticians say that Queueing Theory is closed. Some practitioners feel that there is very little in it for use. In view of this, it seems that after six decades of development it is time for stock taking. It is hoped that a discussion of the problems, achievements and the shortcomings of Queueing Theory will be helpful for both theorists and practitioners by putting things in proper perspective. This paper reviews some of the major strides taken by Queueing Theory with respect to its three constituent problems: (i) Behavioral, (ii) Statistical, and (iii) Operational. If one looks at the general picture of the developments in these area it is hard not to conclude that, in spite of the practitioners' accusations, the systems studied have become more and more realistic over the years. This review makes an attempt to bring this out. An extensive bibliography which is directive in nature rather than exhaustive should be helpful to an interested researcher or a practitioner in identifying the articles of his interest. A discussion of the future of Queueing Theory concludes the paper. [ABSTRACT FROM AUTHOR]

A freight car in the United States spends approximately two-thirds of its time stationary; a significant portion of this time in hump classification yards is spent in queues waiting to be inspected and classified into out-bound trains. This paper describes the development of a model for these queues and the application of the Monte Carlo method to the analysis of these queues for a particular classification yard. An elementary form of feedback is included in the model. Using the model of yard operation, certain methods of improving yard operation are determined. [ABSTRACT FROM AUTHOR]

This paper presents methods for computing point and interval estimates of descriptors of simulated queuing systems. The methods, which rely on the renewal process representation of certain processes, extend the results of CRANE and IGLEHART, and the author. In particular, the paper shows that computation of three sample quantities suffices to generate point and interval estimates for twelve system descriptors. [ABSTRACT FROM AUTHOR]

This paper discusses a class of queuing models in which the service time of a customer at a single-server facility is dependent on the amount that customer has spent queuing for service. A complete investigation is carried out in the particular case of exponential service times with the parameter having a step-function dependency on the waiting time. The stationary waiting-time distribution is investigated for the queue discipline by which customers are served in order of arrival. This class of model is particularly suited for applications wherein customer or item deterioration occurs during waiting, or where the server wishes to provide a more appropriate level of service to counter the negative effects of customer impatience and loss of good will. [ABSTRACT FROM AUTHOR]

The well known formula L= λW relates the time-average number in queue to the expected wait in queue of a customer. This paper specializes a more general formula, denoted by H= λG, in order to obtain relations between moments of L and W other than the first. The basic queue considered is G/G/k with stationary input. The special case where the arrival times form a renewal process and the more special case where they are a Poisson process are also discussed. [ABSTRACT FROM AUTHOR]

This paper studies a priority queuing model in which the processing times of jobs are known upon arrival and preemption without loss of time or processing already accomplished is possible. Jobs are classified into K types according to their lengths, priority is assigned to them according to type and the length of processing remaining, and the paper obtains the expected conditional response times for jobs of each type. [ABSTRACT FROM AUTHOR]

The mean length of a queue is normally estimated by a suitable mean of oh. served values. In order to determine the minimum sample size consistent with some required precision, it is necessary to know the standard error of the sample mean used. Since the observations ire dependent, this standard error is usually greater than the standard error for independent observations, so that a larger sample size is required, This paper derives expressions for the standard errors of some suitable estimators in the cue of finite Markov queues, and examines the efficiencies of these estimators. [ABSTRACT FROM AUTHOR]

In order to discuss scheduling algorithms for time-sharing computer systems, this paper analyzes the M/G/1 queue under the well known round-robin (RR) discipline. Three models are considered: the constant-quantum RR model, the processor-shared (or zero-quantum RR) model, and the variable-quantum RR model. The paper proposes an effective calculating method for obtaining the expected response time under an arbitrary processing-time distribution with overhead. By the theoretical analysis, one can show how the response time is affected by the scheduling and processing-time distributions, as is demonstrated by some typical examples. [ABSTRACT FROM AUTHOR]

This paper compares the waiting times of customers under three priority rules: the order-of-arrival rule, the shortest processing time (within a generation) first, and the longest processing time (within a generation) first. In particular, the covariance matrix of the trivariate distribution of the equilibrium waiting times is obtained explicitly. [ABSTRACT FROM AUTHOR]

This paper finds sufficient conditions for the ergodicity and recurrence of irreducible and aperiodic Markov chains. They extend some of the ones commonly used. The paper also indicates their use in discussing a certain class of queuing problem with state dependent service times. [ABSTRACT FROM AUTHOR]

A fundamental question m long-range planning for the logistic support of an ocean area is the size and location of bases. The present paper proposes a measure of effectiveness, called the 'logistic effectiveness,' for a given set of bases supporting the region. This is done by a maximizing process. Then the sizes of the bases are varied, subject to a budgetary constraint, and an 'optimal base structure' found. For small numbers of bases, for instance three bases, the calculations may be done by hand. Two numerical examples are presented. The paper is intended as a contribution to theory and not for immediate practical application. [ABSTRACT FROM AUTHOR]

This paper starts by observing that any queuing system can be viewed as two symmetric queues, one of customers in line for service, and one of idle clerks, awaiting customers Usually at least one of the queues (the idle clerks) has a finite limit, but examples, such as passengers and taxis at a taxi stand, exist where both queues are unlimited In such cases, if arrival and service rates are independent of queue length, at least one of the queues is unstable and grows indefinitely as time passes In practice there has to be some factor that limits queue length, and a possible mechanism is to assume that both passengers and taxis become impatient and will leave if, after some fixed amount of time, they have not been 'serviced ' The equations governing such a system are developed and steady-state solutions are found It is shown that steady-state solutions always exist for both queues, the means and variances (which are finite) are given In the last part of the paper an application to inventory theory is suggested Here the backlog of orders corresponds to the queue of customers, and items in stock to the idle clerks It is assumed that orders not filled in a certain time are cancelled and that items are perishable and cannot be sold if stocked too long. [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Production Research is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The steel industry is one of the first industries where operational research was successfully applied. The objective of the present paper is to summarize such applications high-lighting benefits and difficulties involved in the studies and in their subsequent implementation.
The paper is divided into three sections. The first section contains a brief survey of the reported case studies in literature pertaining to the application of O.R. techniques and methodology in production problems in the steel industry. The second section deals with a few case studies which illustrate the model building procedures and their usefulness in real life.
The final section of the paper is devoted to a discussion of the potential areas where O.R. techniques and methodology can be fruitfully applied in modeling production processes for control purposes. [ABSTRACT FROM AUTHOR]

This article presents information about various books. Some of the books include: "An Introduction to Equilibrium Thermodynamics," by Robert P. Bauman, "Decision and Control: The Meaning of Operational Research and Management Cybernetics," by Stafford Beer, "A Bibliography of Critical Path Methods," by J. Farmer, "Applied Boolean Algebra: An Elementary Introduction," 2nd ed., by Franz E. Hohn, "Manpower Planning: Operational Research and Personnel Research," edited by W.N. Jessop, and "Applied Queuing Theory," by Alec M. Lee.

The analysis of tandem queues in which the output of each stage immediately becomes the input to the next is, in general, quite difficult. Although the analytic solution for the steady-state departure distribution from an M/M/N queue is well-known and that of an M/G/1 queue can be obtained if the analyst is willing to view it through a 'Laplacian curtain,' the list of existing analytic solutions is not long. Some analytic 'tricks' exist, but their utility is usually limited to the single-server queue. The treatment of tandem queues not fitting into these categories has been largely left to simulation. Yet this approach has its drawbacks. It is expensive and involves difficulties in designing and analyzing the simulation experiment. Approximation techniques are beginning to emerge as a wiser, faster, cheaper, and less troublesome alternative to simulation. In this paper we develop approximate solutions for average steady-state queue length in four different but related tandem queues that arise in connection with the service sys-of an air terminal complex. The approximate expressions obtained are validated by simulation. [ABSTRACT FROM AUTHOR]

This paper presents computationally efficient techniques for approximating several behavioral aspects of the M[sup X](t)/E[sub Y]/1 queue. The nonstationary arrival stream allows demands for service to follow different distributions over different time intervals. Specific performance characteristics evaluated are the first two moments of queue length, virtual waiting time, and system utilization. These are based on approximating the distribution of Q(t) at the time points E[T[sub n]] by the distribution of Q[sub n], where T[sub n] is the epoch of the nth departure and Q[sub n] = Q(T[sub n] + 0). The results are in agreement with those obtained by simulation but require much less computing time. Sample results are presented for both stationary and nonstationary examples. [ABSTRACT FROM AUTHOR]

This paper presents an approximate procedure for computing selected performance characteristics of an urban emergency service system. Based on a recently developed hypercube queuing model, the procedure requires for N servers solution of only N simultaneous equations, rather than 2[sup N] as in the exact model. The procedure relies on the theory of M/M/N queues in which servers are selected randomly and without replacement until the first available (free) server is found. The underlying model is intended for analyzing problems of vehicle location and response district design in urban emergency services, includes interdistrict as well as intradistrict responses, and allows computation of several point-specific as well as area-specific performance measures. [ABSTRACT FROM AUTHOR]

This paper provides simple, readily computable approximations for the limiting behavior of the waiting-time process in a queuing system having a certain scheme of nonindependent interarrival times. Its results are obtained without recourse to stringent distribution assumptions. [ABSTRACT FROM AUTHOR]

This paper studies a control policy for an M/G/1 nonpreemptive-priority queuing system with removable server and two priority classes. This policy turns off the server when the system is empty and turns him on when a given linear combination of the numbers of class 1 and class 2 customers in the system exceeds a certain value. Expressions for the long-run average numbers of class 1 and class 2 customers in the system are derived. [ABSTRACT FROM AUTHOR]

This paper discusses the M/M/1 queue embedded in a Markovian environment (or, subject to extraneous phase changes). It studies the busy period, equilibrium conditions, and emptiness probabilities by using analytic matric functions, and makes comparisons with the work of NEUTS and of NAOR and YECHIALI. [ABSTRACT FROM AUTHOR]

This paper presents a new class of queuing models. There are n distinct types of customers and n distinct types of service facilities. Some customers can be processed at any service facility, but other customer types can only use selected ones among the service-facility types. This class of model is named 'lane selection,' abbreviated LS, since the arriving customers with some freedom of choice must select the queue, or lane, in which they are to be processed through the system. It is shown by example that many physical situations are represented more accurately by this model than by more conventional ones. However, in analysis, the LS concept raises many theoretical difficulties. For a number of special cases, this paper obtains in explicit form as functions of the model parameters the mean queue lengths and waiting times for the different classes of customers. [ABSTRACT FROM AUTHOR]

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In modern telephone systems utilizing computers, the realization of a single server feedback queueing system often arises. In this paper, it is assumed that an originating or transferred call to such a system requires a number of different services before leaving the system as a completed or rejected call. A customer may also repeat a portion of his services, omit some services, or leave the system after any service with some assigned probabilities. In this paper, we present a theorem on the joint multi-variate queue length distribution, in a system with N services or queues, arbitrary priorities, and a general probabilistic transition matrix inter-connecting the various queues. [ABSTRACT FROM AUTHOR]

This paper derives the form of a minimal cost rate stationary operating policy for an M/M/I queueing system with K possible service rates. The two costs of the system are a general cost rate dependent on the state of the system and a cost rate associated with each of the possible service rates. The optimal policy is completely characterized by K - 1 numbers. The optimal service rate is shown to be nondecreasing in the state of the system. [ABSTRACT FROM AUTHOR]

This paper attempts to coordinate at the macro level the research potential and the development capability of an organization in a competitive environment. New product ideas generate from various sources of research which are then processed (preliminary screening, market appraisal, technical development etc.) by the development section. In view of the randomness present in the above process, a backlog of ideas will normally be present awaiting development. The longer the delay in processing them, the greater are the chances of a competitor introducing the product in the meantime. Simple queueing models are set up which abstract the essence of the problem, and reveal the causal relationships of the underlying structure. The decision variable (relationship of the research rate to the development rate) is optimized, and its sensitivity to changes in the parameters describing the environment is examined. Generalizations of the approach using Monte-Carlo methods are also indicated. [ABSTRACT FROM AUTHOR]

This paper presents results for queueing systems that are characterized by poisson arrival epochs with χ (a random variable) arrivals at each epoch, exponential service times and c servers. The steady state probabilities, the probability of blocking (not being served immediately) for both loss and delay systems are investigated. In addition, the average delay, the variance of the delay and the delay distribution for first-come-served by batches and arbitrary order of service within batches are presented. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of a queueing process involving two classes of customers where the arrival mechanism of each class is subject to a particular control doctrine based on the queue length. Expressions are obtained for the equilibrium distribution of the queue length, the expected queue length and other characteristics which measure the effectiveness of the control doctrine. [ABSTRACT FROM AUTHOR]

The paper investigates in detail a single server single queue time-sharing system with homogeneous Poisson arrivals and exponentially distributed service times. The important variables affecting the design and operation of the system were investigated, and the results are given in terms of steady-state expectations and distribution transforms. An attempt is made to demonstrate the influence of various system's parameters on the overall performance. Special attention is given to optimization with respect to quantum size. It is hoped that some of the results may serve as guidelines in the design and operation of time-sharing systems. [ABSTRACT FROM AUTHOR]

In this paper we utilize traditional microeconomic theory and elementary queuing theory to develop a computer simulation model of a single-product, multi-process firm. One of our objectives is to demonstrate that the body of economic theory known as the "theory of the firm" may be used to provide a convenient frame of reference in applying some of the more recently developed analytical tools of operations research and computer technology to the analysis of the behavior of the firm. The static equilibrium model of the firm presented in Value and Capital by J. R. Hicks is taken as a point of departure in constructing a simulation model in which (1) the time interval between the arrival of orders at the firm is a stochastic variate with a known probability distribution, (2) each order which the firm receives must pass through n processes before it is transformed into a single unit of output, and (3) the time interval which an order spends at the jth process (j = 1, ..., n) is a stochastic variate with a known probability distribution. [ABSTRACT FROM AUTHOR]