Stability and tail behavior of redundancy systems with processor sharing

We consider an M/G/1 queue that is idle at time 0. The number of customers sampled at an independent exponential time is shown to have the same geometric distribution under the preemptive-resume last-in-first-out and the processor-sharing disciplines. Hence, the marginal distribution of the queue length at any time is identical for both disciplines. We then give a detailed analysis of the time until the first departure for any symmetric queueing discipline. We characterize its distribution and show that it is insensitive to the service discipline. Finally, we study the tail behavior of this distribution.

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Tail behavior of conditional sojourn times in Processor-Sharing queues

Queueing Systems ◽

10.1007/s11134-006-9007-4 ◽

2006 ◽

Vol 55 (2) ◽

pp. 107-121 ◽

Cited By ~ 3

Author(s):

Regina Egorova ◽

Bert Zwart

Keyword(s):

Processor Sharing ◽

Tail Behavior ◽

Sojourn Times ◽

Processor Sharing Queues

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Some Time-Dependent Properties of Symmetric M/G/1 Queues

Journal of Applied Probability ◽

10.1239/jap/1110381382 ◽

2005 ◽

Vol 42 (1) ◽

pp. 223-234 ◽

Cited By ~ 6

Author(s):

Offer Kella ◽

Bert Zwart ◽

Onno Boxma

Keyword(s):

Queue Length ◽

Marginal Distribution ◽

Geometric Distribution ◽

Time Dependent ◽

Service Discipline ◽

Processor Sharing ◽

Tail Behavior ◽

Exponential Time ◽

Preemptive Resume ◽

Number Of Customers

We consider an M/G/1 queue that is idle at time 0. The number of customers sampled at an independent exponential time is shown to have the same geometric distribution under the preemptive-resume last-in-first-out and the processor-sharing disciplines. Hence, the marginal distribution of the queue length at any time is identical for both disciplines. We then give a detailed analysis of the time until the first departure for any symmetric queueing discipline. We characterize its distribution and show that it is insensitive to the service discipline. Finally, we study the tail behavior of this distribution.

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Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

Journal of Applied Probability ◽

10.1017/s0021900200002965 ◽

2007 ◽

Vol 44 (02) ◽

pp. 285-294 ◽

Cited By ~ 2

Author(s):

Qihe Tang

Keyword(s):

Asymptotic Formula ◽

Continuous Time ◽

Heavy Tails ◽

Tail Behavior ◽

Renewal Model ◽

Discounted Aggregate Claims ◽

Aggregate Claims ◽

Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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