A single server queue with gated processor-sharing discipline

1989 ◽  
Vol 4 (3) ◽  
pp. 249-261 ◽  
Author(s):  
Kiran M. Rege ◽  
Bhaskar Sengupta
Keyword(s):  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Server Queue

Equilibrium Strategies for Processor Sharing and Random Queues with Relative Priorities

1997 ◽  
Vol 11 (4) ◽  
pp. 403-412 ◽  
Author(s):  
Moshe Haviv ◽  
Jan van der Wal
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Price ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Relative Priority ◽  
Equilibrium Strategies ◽  
Service Disciplines ◽  
Server Queue

We consider a memoryless single-server queue in which users can purchase relative priority so as to reduce their expected waiting costs, which are linear with time. Relative priority is given in proportion to a price paid by customers present in the system. For two service disciplines, (weighted) processor sharing and (weighted) random entrance, we find the unique pure and symmetric Nash equilibrium price paid by the customers.

scholarly journals A FLUID LIMIT FOR PROCESSOR-SHARING QUEUES WEIGHTED BY FUNCTIONS OF REMAINING AMOUNTS OF SERVICE

2019 ◽  
pp. 1-8
Author(s):  
Yingdong Lu
Keyword(s):  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Fluid Limit ◽  
Scheduling Policy ◽  
Server Queue ◽  
Processor Sharing Queues

Abstract We study a single server queue under a processor-sharing type of scheduling policy, where the weights for determining the sharing are given by functions of each job's remaining service (processing) amount, and obtain a fluid limit for the scaled measure-valued system descriptors.

Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (4) ◽  
pp. 943-963 ◽  
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

scholarly journals PROPERTIES OF THE GITTINS INDEX WITH APPLICATION TO OPTIMAL SCHEDULING

2011 ◽  
Vol 25 (3) ◽  
pp. 269-288 ◽  
Author(s):  
Samuli Aalto ◽  
Urtzi Ayesta ◽  
Rhonda Righter
Keyword(s):  
Specific Problem ◽  
Optimal Scheduling ◽  
Single Server ◽  
Processor Sharing ◽  
Gittins Index ◽  
Single Server Queue ◽  
Index Policy ◽  
Special Cases ◽  
The Family ◽  
Server Queue

We consider the optimal scheduling problem for a single-server queue without arrivals. We allow preemptions, and our purpose is to minimize the expected flow time. The optimal nonanticipating discipline is known to be the Gittins index policy, which, however, is defined in an implicit way. Until now, its general behavior in this specific problem has been characterized only in a few special cases. In this article, we give as complete a characterization as possible. It turns out that the optimal policy always belongs to the family of multilevel processor sharing disciplines.

Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (04) ◽  
pp. 943-963
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

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