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.

On stability of queueing networks with job deadlines

2003 ◽  
Vol 40 (2) ◽  
pp. 293-304 ◽  
Author(s):  
Amy R. Ward ◽  
Nicholas Bambos
Keyword(s):  
Sojourn Time ◽  
Queueing Networks ◽  
Single Server ◽  
Single Server Queue ◽  
Interesting Phenomenon ◽  
Single Node ◽  
Service Disciplines ◽  
Server Queue ◽  
Weakly Stable ◽  
Networks Of Queues

In this paper, we consider a single-server queue with stationary input, where each job joining the queue has an associated deadline. The deadline is a time constraint on job sojourn time and may be finite or infinite. If the job does not complete service before its deadline expires, it abandons the queue and the partial service it may have received up to that point is wasted. When the queue operates under a first-come-first served discipline, we establish conditions under which the actual workload process—that is, the work the server eventually processes—is unstable, weakly stable, and strongly stable. An interesting phenomenon observed is that in a nontrivial portion of the parameter space, the queue is weakly stable, but not strongly stable. We also indicate how our results apply to other nonidling service disciplines. We finally extend the results for a single node to acyclic (feed-forward) networks of queues with either per-queue or network-wide deadlines.

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

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.

On stability of queueing networks with job deadlines

2003 ◽  
Vol 40 (02) ◽  
pp. 293-304
Author(s):  
Amy R. Ward ◽  
Nicholas Bambos
Keyword(s):  
Sojourn Time ◽  
Queueing Networks ◽  
Single Server ◽  
Single Server Queue ◽  
Interesting Phenomenon ◽  
Single Node ◽  
Service Disciplines ◽  
Server Queue ◽  
Weakly Stable ◽  
Networks Of Queues

In this paper, we consider a single-server queue with stationary input, where each job joining the queue has an associated deadline. The deadline is a time constraint on job sojourn time and may be finite or infinite. If the job does not complete service before its deadline expires, it abandons the queue and the partial service it may have received up to that point is wasted. When the queue operates under a first-come-first served discipline, we establish conditions under which the actual workload process—that is, the work the server eventually processes—is unstable, weakly stable, and strongly stable. An interesting phenomenon observed is that in a nontrivial portion of the parameter space, the queue is weakly stable, but not strongly stable. We also indicate how our results apply to other nonidling service disciplines. We finally extend the results for a single node to acyclic (feed-forward) networks of queues with either per-queue or network-wide deadlines.

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.

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