Decomposition formulas for single server queues with vacations : a unified approach by the rate conservation law

1994 ◽  
Vol 10 (2) ◽  
pp. 389-413 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
Conservation Law ◽  
Single Server ◽  
Unified Approach ◽  
Single Server Queues ◽  
Queues With Vacations

scholarly journals A Unifying Conservation Law for Single-Server Queues

2007 ◽  
Vol 44 (04) ◽  
pp. 1078-1087 ◽  
Author(s):  
Urtzi Ayesta
Keyword(s):  
Conservation Laws ◽  
Service Time ◽  
Conservation Law ◽  
Single Server ◽  
Processor Sharing ◽  
Time Sharing ◽  
Single Class ◽  
Class Time ◽  
Single Server Queues ◽  
General Service

We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating disciplines with exponential service time distributions and (ii) nonpreemptive nonanticipating disciplines with general service time distributions. The unifying conservation law we develop generalizes already existing conservation laws. In addition, it covers popular nonanticipating multi-class time-sharing disciplines such as discriminatory processor sharing (DPS) and generalized processor sharing (GPS) with general service time distributions. As an application, we show that the unifying conservation law can be used to compare the expected unconditional response time under two scheduling disciplines.

scholarly journals A Unifying Conservation Law for Single-Server Queues

2007 ◽  
Vol 44 (4) ◽  
pp. 1078-1087 ◽  
Author(s):  
Urtzi Ayesta
Keyword(s):  
Conservation Laws ◽  
Service Time ◽  
Conservation Law ◽  
Single Server ◽  
Processor Sharing ◽  
Time Sharing ◽  
Single Class ◽  
Class Time ◽  
Single Server Queues ◽  
General Service

We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating disciplines with exponential service time distributions and (ii) nonpreemptive nonanticipating disciplines with general service time distributions. The unifying conservation law we develop generalizes already existing conservation laws. In addition, it covers popular nonanticipating multi-class time-sharing disciplines such as discriminatory processor sharing (DPS) and generalized processor sharing (GPS) with general service time distributions. As an application, we show that the unifying conservation law can be used to compare the expected unconditional response time under two scheduling disciplines.

scholarly journals BOUNDS AND AN APPROXIMATION FOR SINGLE SERVER QUEUES

1983 ◽  
Vol 26 (2) ◽  
pp. 118-134 ◽  
Author(s):  
Jeyaveerasingam George Shanthikumar
Keyword(s):  
Single Server ◽  
Single Server Queues

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

1991 ◽  
Vol 28 (02) ◽  
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.

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