An Approximate Formula for Waiting Time in Single Server Queues

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

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A Characterization of Waiting Time Performance Realizable by Single-Server Queues

Operations Research ◽

10.1287/opre.28.3.810 ◽

1980 ◽

Vol 28 (3-part-ii) ◽

pp. 810-821 ◽

Cited By ~ 95

Author(s):

E. G. Coffman ◽

I. Mitrani

Keyword(s):

Waiting Time ◽

Single Server ◽

Time Performance ◽

Single Server Queues

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Stationary Waiting-Time Distributions for Single-Server Queues

The Annals of Mathematical Statistics ◽

10.1214/aoms/1177704365 ◽

1962 ◽

Vol 33 (4) ◽

pp. 1323-1339 ◽

Cited By ~ 38

Author(s):

R. M. Loynes

Keyword(s):

Waiting Time ◽

Single Server ◽

Waiting Time Distributions ◽

Single Server Queues ◽

Stationary Waiting Time

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An approximation for the waiting time distribution in single server queues

Naval Research Logistics Quarterly ◽

10.1002/nav.3800270207 ◽

1980 ◽

Vol 27 (2) ◽

pp. 223-230

Author(s):

Irwin Greenberg

Keyword(s):

Waiting Time ◽

Time Distribution ◽

Single Server ◽

Waiting Time Distribution ◽

Single Server Queues

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The existence of waiting time moments for single server queues with mixed renewal and poisson inputs

Series Statistics ◽

10.1080/02331888108801584 ◽

1981 ◽

Vol 12 (2) ◽

pp. 225-232 ◽

Cited By ~ 1

Author(s):

Siegfried Schönherr

Keyword(s):

Waiting Time ◽

Single Server ◽

Single Server Queues

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Single-Server Queues with Service Time Dependent on Waiting Time

Operations Research ◽

10.1287/opre.21.2.610 ◽

1973 ◽

Vol 21 (2) ◽

pp. 610-616 ◽

Cited By ~ 26

Author(s):

M. Posner

Keyword(s):

Waiting Time ◽

Service Time ◽

Time Dependent ◽

Single Server ◽

Single Server Queues

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The stationary waiting time and other variables in single-server queues with specialities at the beginning of a busy period

Applicationes Mathematicae ◽

10.4064/am-13-4-465-479 ◽

1973 ◽

Vol 13 (4) ◽

pp. 465-479

Author(s):

G. Siegel

Keyword(s):

Waiting Time ◽

Busy Period ◽

Single Server ◽

Single Server Queues ◽

Stationary Waiting Time

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Finiteness of Waiting-Time Moments in General Stationary Single-Server Queues

The Annals of Applied Probability ◽

10.1214/aoap/1177005585 ◽

1992 ◽

Vol 2 (4) ◽

pp. 987-1008 ◽

Cited By ~ 20

Author(s):

D. J. Daley ◽

T. Rolski

Keyword(s):

Waiting Time ◽

Single Server ◽

Single Server Queues

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Convex ordering of the attained waiting times in single-server queues and related problems

Journal of Applied Probability ◽

10.2307/3214878 ◽

1991 ◽

Vol 28 (2) ◽

pp. 433-445

Author(s):

Masakiyo Miyazawa ◽

Genji Yamazaki

Keyword(s):

Waiting Time ◽

Time Distribution ◽

Waiting Times ◽

Service Discipline ◽

Single Server ◽

Waiting Time Distribution ◽

Convex Order ◽

Convex Ordering ◽

Single Server Queues ◽

Service Disciplines

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

Download Full-text