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Priority Assignment in Waiting Line Problems
413
Citations
0
References
1954
Year
Mathematical ProgrammingCrowded Communication ChannelEngineeringQueueing TheoryOperations ResearchOperations Research SocietySystems EngineeringLogisticsPriority AssignmentCombinatorial OptimizationQuantitative ManagementOperations ManagementInteger ProgrammingQueueing SystemsScheduling ProblemScheduling (Operating Systems)Performance ModelingBusinessScheduling (Production Processes)Queuing TheoryScheduling (Project Management)
In many queueing scenarios, a unit’s position is governed by priority rather than arrival time, as illustrated by message transmission lines where urgent messages preempt routine ones, and units can advance or recede over time depending on service and higher‑priority arrivals. The study aims to evaluate priority assignment procedures by analyzing the average waiting time from arrival to service for units of a given priority. The authors derive analytic expressions for the average waiting time in two settings: a single‑channel system with arbitrary service times and a multi‑channel system with exponential service times, assuming random arrivals. Published in Operations Research (ISSN 0030‑364X), the article appeared in the Journal of the Operations Research Society of America (ISSN 0096‑3984) from 1952 to 1955.
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-channel system in which the servicing times are exponentially distributed (Eq. 6). In both cases it is assumed that arrivals occur at random. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.