Priority Assignment in Waiting Line Problems

Cobham, Alan

doi:10.1287/opre.2.1.70

Cited by 327 publications

(132 citation statements)

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“…As was noted earlier in the previous discussion, the determination of the mean system sizes and waiting times can be found via a direct cxpectcd-valuc procedure such as that due to Cobham [1954] or through the more classical differential-differenceequation method such as that found in Morse [195S]. Cobham's approach to the mean delay for display was selected since it is more straightforward and can, in fact, be just as well used to handle multiple priorities as two priorities.…”

Section: A-10 Results For Nonpreemptive Exponential Queues With Many mentioning

confidence: 99%

Implementation of a Model of Requisition Processing for the Ships Supply Support Study

Lady¹

1973

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Steps in the Methodology 2-3Step I: Eliminate Cycles from Flow Matrix 2-5Step II: Establish Work Load Factors 2-5Step III: Establish Capacity Factors 2-6Step IV: Implement Multipriority Queueing Model 2-10Step V: Path Analysis 2-10Step VI: Establish Frequency Distribution of Throughput Times Per Path 2-11Step VII: Calculate Distribution of System Throughput Times . . 2-11 Illustration of the Methodology 2-12Step I: Eliminate Cycles 2-12Step II: Establish Work Load Factors 2-13Step HI: Establish Capacities 2-15Step IV: Implement Multipriority Queueing Model 2-16 Steps V and VI: Path Analysis and Path Frequency Distributions. 2-23Step VII: System Throughput Times 2-29 MODELING REQUISITION PROCESSING AT SPCC 3-1 rtStep I: Eliminate Cycles from Flow Matrix 3-3Step V: Path Analysis 3-4Step HE: Establish Capacity Factors 3-7Step II: Establish Work Load Factors 3-9Step IV: Implement Multipriority Queueing Model 3-9Outputs of the Multipriority Queueing Model 3-16Step Generally, the data describing materials handling operations revealed very modest backlogs. Confidence in the throughput times predicted by an extrapolation of materials handling models was enhanced by the fact that the models could be designed to closely replicate the materials handling process. Only that portion of throughput time associated with requisition processing appeared to offer complexities which would not submit to main force analytic techniques. MODELING REQUISITION PROCESSINGStudy requisition processing at inventory control points (ICPs) and stock points revealed long waiting times not apparently related to servicing the requisitions. Certain of these times could be explained by policy and administrative procedures not related to resource levels. However, in the initial modeling efforts waiting times due to backlogs could not be explained by the relatively simple queueing theory models attempted. Several factors could explain the failure to model backlogs:• the queueing models attempted did not take into account the system of priorities under which requisitions were processed,• the resources dedicated to requisition processing are often used in a number of other capacities,• the assumptions about work load arrival rate and service time distributions used by the queueing model might be unrealistic, and• the backlogs might be contrived by supply system personnel for any of a number of reasons ranging from a desire to efficiently use personnel to foster job security. The problem with the status file records as kept was that the prior "history" of a requisition was erased when the file was updated. An investigation by Fleet Material Support Office (FMSO) personnel revealedthat all entries to the status file were retained for 30 days at the inventory control points in a concentrated data format. A very extensive and ambitious programming 1-3 task was undertaken at FMSO to extract these data and generate the outputs enumerated above. A program was successfully completed and a data extraction and data analysis effort was implemented for data describi...

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Section: A-10 Results For Nonpreemptive Exponential Queues With Many mentioning

confidence: 99%

Implementation of a Model of Requisition Processing for the Ships Supply Support Study

Lady¹

1973

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“…If the code indicates a (2), i.e. , moderate degree of danger to property, then it is mapped as a (2) .…”

Section: Waiting Timementioning

confidence: 99%

A search and rescue simulation model for the United States Coast Guard :

Karp¹,

Maltese²

1971

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and accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the develop ment of the National Standard Reference Data System and a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum accessibility to the scientific information of the world, and directs the public information activities of the Bureau User Control in PREPRO. In summary, the simulation approach has been selected as the methodology for studying the SAR problem because of its several advantages few disadvantages and high probability of success.-13 -3.Design of the Simulation These added events will, for example, allow a resource enroute to a case to be diverted to another case of higher priority (i.e., interrupt)It will also allow a case in progress to have its priority change (in either direction) to reflect changing conditions and assistance already received.Since the Coast Guard desired to investigate alternative resource mixes, it was not sufficient that the simulation merely assign the same resource type to a given case as was assigned historically. Therefore, a highly sophisticated set of resource assignment algorithms had to be designed such that the preferred resource (or resources, for a multi-resource case) is selected from all the existing resources being simulated for assignment to each case. The provision for priority interrupt, of course, further complicates these algorithms.The resource assignment algorithm for long* search cases is *Cases involving searches of less than one-half hour duration are handled separately.-17 -somewhat more complex than for non-search cases because of the widely differing capabilities for search among the various resource types.However, the servicing of a search case in the model is less detailed than the servicing of a non-search case. This is due to the limited data available in the data base on how the search was carried out (e.g., search pattern, track width, etc. are not given) and also due to the relatively minor incidence of long search cases in the overall SAR system.Only a small fraction of the total SAR caseload involves a long search requirement. However, when such a case does come up, it consumes a considerable amount of (usually expensive) resource time.Therefore, the objective of servicing long search cases in the simulation was mainly to account for this resource utilization when the relatively unlikely event of a long search comes up --because the resources occupied on a search case will not be available (unless interrupted)for the more common non-search cases. Hence the level of detail need not be as fine for these long search cases. Selection of Programming LanguageAs a result of a comprehensive analysis of the available programming languages and associated computer systems, the SIMSCRIPT 1.5 language was chosen for basic operational module of SARSIM. A report entitled:"Selection of Programming Language," ...

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“…[7,8,16]) and single-and multiserver priority queues received much attention. Most of the earlier studies concentrate on the transforms of marginal system characteristics such as the queue length and waiting time of a specific priority class.…”

Section: Introductionmentioning

confidence: 99%

Joint queue length distribution of multi-class, single-server queues with preemptive priorities

et al. 2015

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In this paper we analyze an M/M/1 queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic techniques and probabilistic arguments, we develop a recursive method for the exact determination of the equilibrium joint queue length distribution. The method is applied to a spare parts logistics problem to illustrate the effect of setting repair priorities on the performance of the system. We conclude by briefly indicating how the method can be extended to an M/M/1 queueing system with non-preemptive priorities between customer classes.

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Priority Assignment in Waiting Line Problems

Cited by 327 publications

References 0 publications

Implementation of a Model of Requisition Processing for the Ships Supply Support Study

Implementation of a Model of Requisition Processing for the Ships Supply Support Study

A search and rescue simulation model for the United States Coast Guard :

Joint queue length distribution of multi-class, single-server queues with preemptive priorities

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