Evaluation of the Total Time in System in a Preempt/Resume Priority Queue via a Modified Lindley Process.

Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

Advances in Applied Probability ◽

10.1017/s0001867800021649 ◽

1983 ◽

Vol 15 (04) ◽

pp. 840-856 ◽

Cited By ~ 2

Author(s):

J. Keilson ◽

U. Sumita

Keyword(s):

Time Distribution ◽

Arrival Rate ◽

Priority Queue ◽

Service Time Distribution ◽

Transform Method ◽

Laguerre Transform ◽

Poisson Stream ◽

Lindley Process ◽

Theoretical Results ◽

Time Sequences

A Poisson stream of arrival rate λI and service-time distribution A I(x) has preempt/resume priority over a second stream of rate λII and distribution A II(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.

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Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

Advances in Applied Probability ◽

10.2307/1427327 ◽

1983 ◽

Vol 15 (4) ◽

pp. 840-856 ◽

Cited By ~ 13

Author(s):

J. Keilson ◽

U. Sumita

Keyword(s):

Time Distribution ◽

Arrival Rate ◽

Priority Queue ◽

Service Time Distribution ◽

Transform Method ◽

Laguerre Transform ◽

Poisson Stream ◽

Lindley Process ◽

Theoretical Results ◽

Time Sequences

A Poisson stream of arrival rate λI and service-time distribution AI(x) has preempt/resume priority over a second stream of rate λII and distribution AII(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.

Download Full-text