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Journal ArticleDOI

Work-conserving priorities

01 Aug 1970-Journal of Applied Probability (Cambridge University Press (CUP))-Vol. 7, Iss: 2, pp 327-337
About: This article is published in Journal of Applied Probability.The article was published on 1970-08-01. It has received 77 citations till now. The article focuses on the topics: Work (electrical).
Citations
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Journal ArticleDOI
TL;DR: This paper presents a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.
Abstract: In many stochastic models, particularly in queueing theory, Poisson arrivals both observe (see) a stochastic process and interact with it. In particular cases and/or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state. In this paper, we present a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.

1,226 citations


Additional excerpts

  • ...WOLFF, R. W. 1970....

    [...]

Journal ArticleDOI
TL;DR: Stochastic scheduling problems in which the processing times of jobs are independent exponentially distributed random variables, the release dates arerandom variables with an arbitrary joint distribution, and the due dates are random variables with a joint distribution that satisfies certain conditions are considered.
Abstract: We consider stochastic scheduling problems in which the processing times of jobs are independent exponentially distributed random variables, the release dates are random variables with an arbitrary joint distribution, and the due dates are random variables with a joint distribution that satisfies certain conditions. Our development establishes simple policies that minimize such criteria as the expected weighted sum of completion times and the expected weighted number of late jobs. These results contrast markedly with the deterministic counterparts of these models for which no polynomial time algorithms are known.

210 citations

Journal ArticleDOI
Hisashi Kobayashi1, A. Konheim1
TL;DR: The present paper is intended to review the state of affairs of analytic methods, queueing analysis techniques in particular, which are essential to modeling of computer communication systems.
Abstract: Modeling and performance prediction are becoming increasingly important issues in the design and operation of computer communications systems. Complexities in their configuration and sophistications in resource sharing found in today's computer communications demand our intensive effort to enhance the modeling capability. The present paper is intended to review the state of affairs of analytic methods, queueing analysis techniques in particular, which are essential to modeling of computer communication systems. First we review basic properties of exponential queueing systems, and then give an overview of recent progress made in the areas of queueing network models and discrete-time queueing systems. A unified treatment of buffer storage overflow problems will be discussed as an application example, in which we call attention to the analogy between buffer behavior and waiting time in the GI/G/1 queue. Another application deals with the analysis of various multiplexing techniques and network configuration. An extensive reference list of the subject fields is also provided.

185 citations

Journal ArticleDOI
Onno Boxma1
TL;DR: This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present.
Abstract: One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions.

182 citations

Onno Boxma1
01 Jan 1989
TL;DR: In this article, a decomposition of the amount of work in a single-server multi-class service system with interruptions is presented, where the server's activities may be interrupted although work is still present.
Abstract: One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions.

164 citations

References
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Journal ArticleDOI
TL;DR: In this paper, it was shown that if the three means are finite and the corresponding stochastic processes strictly stationary, and if the arrival process is metrically transitive with nonzero mean, then L = λW.
Abstract: In a queuing process, let 1/λ be the mean time between the arrivals of two consecutive units, L be the mean number of units in the system, and W be the mean time spent by a unit in the system. It is shown that, if the three means are finite and the corresponding stochastic processes strictly stationary, and, if the arrival process is metrically transitive with nonzero mean, then L = λW.

2,536 citations

Book
01 Jan 1968

654 citations

01 Jan 1961

647 citations

Journal ArticleDOI
TL;DR: The average elapsed time between the arrival in the line of a unit of a given priority and its admission to the facility for servicing is useful in evaluating the procedure by which priority assignments are made.
Abstract: There are several commonly occurring situations in which the position of a unit or member of a waiting line is determined by a priority assigned to the unit rather than by its time of arrival in the line. An example is the line formed by messages awaiting transmission over a crowded communication channel in which urgent messages may take precedence over routine ones. With the passage of time a given unit may move forward in the line owing to the servicing of units at the front of the line or may move back owing to the arrival of units holding higher priorities. Though it does not provide a complete description of this process, the average elapsed time between the arrival in the line of a unit of a given priority and its admission to the facility for servicing is useful in evaluating the procedure by which priority assignments are made. Expressions for this quantity are derived for two cases—the single-channel system in which the unit servicing times are arbitrarily distributed (Eq. 3) and the multiple-cha...

439 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of service interruptions on a single-server system with stationary compound Poisson input and general independent service times is studied, the latter being subject to random interruptions of independently but otherwise arbitrarily distributed durations.
Abstract: SUMMARY A single-server system with stationary compound Poisson input and general independent service times, the latter being subject to random interruptions of independently but otherwise arbitrarily distributed durations, is studied. For a variety of service-interruption interactions (including the preemptiverepeat) the distributions of busy period duration, of queue length, and of waiting time are characterized by transforms and by moments. Applications are made to priority scheduling problems. MANY situations in which waiting lines develop are characterized by the occurrence of interruptions in customer service. Such interruptions may be caused by breakdowns of a machine that provides service, for example, an electronic computer. Also, if certain customers are assigned priority, then the appearance of one of these may bring about an interruption in the servicing of low-priority customers. In practice it would not be surprising to find systems that experience interruptions of both sorts. In this paper we consider the effect of service interruptions upon a waiting-line process of the following kind: customers appear in accordance with a stationary compound Poisson process (i.e. bunches of customers arrive randomly), and are served in turn by a single facility. The basic customer servicing times are independently, identically, but otherwise arbitrarily, distributed. Interruptions appear at random, in the sense that, if the system is currently free of interruption, the time until the next interruption occurs is exponentially distributed. Interruption durations are identically, independently and arbitrarily distributed. Without interruptions the process described has been discussed by Gaver (1959); the present paper is an adaptation of the approach of the latter paper to the needs of the interruption problem. Previous treatments of similar problems, emphasizing priorities, have been given by Cobham (1954), Stephan (1956), Kesten and Runnenberg (1957), White and Christie (1958), Morse (1958, Chapter 9) and Miller (1960). The influence of service interruptions upon waiting-line behaviour cannot be investigated without specifying in detail the interaction between the interruption process and the service process. Throughout the present paper it will be assumed that all interruptions occurring during a particular customer's service period must take effect during, or immediately after, that period. Thus interruptions may be preemptive, summarily breaking in upon a service in progress, or postponable to the end of that period, but not beyond. If interruptions are preemptive it may be possible to resume service from the point at which interruption took place when the interruption is cleared; such an interaction (between service and interruption) is called

424 citations