Large Deviations for the Infinite Server Queue in Heavy Traffic

1995 ◽  
pp. 387-394 ◽  
Author(s):  
Peter W. Glynn
Keyword(s):  
Large Deviations ◽  
Heavy Traffic ◽  
Infinite Server ◽  
Server Queue

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

Stationary Analysis of Infinite Server Queue with Batch Service

2021 ◽  
pp. 411-424
Author(s):  
Ayane Nakamura ◽  
Tuan Phung-Duc
Keyword(s):  
Batch Service ◽  
Infinite Server ◽  
Stationary Analysis ◽  
Server Queue

scholarly journals An infinite-server queue influenced by a semi-Markovian environment

2008 ◽  
Vol 61 (1) ◽  
pp. 65-84 ◽  
Author(s):  
Brian H. Fralix ◽  
Ivo J. B. F. Adan
Keyword(s):  
Markovian Environment ◽  
Infinite Server ◽  
Server Queue

Transient behavior of coverage processes by applications to the infinite-server queue

1993 ◽  
Vol 30 (3) ◽  
pp. 589-601 ◽  
Author(s):  
Sid Browne ◽  
J. Michael Steele
Keyword(s):  
Line Segment ◽  
Busy Period ◽  
Queueing System ◽  
Transient Behavior ◽  
Infinite Server ◽  
Coverage Process ◽  
Server Queue

We obtain the distribution of the length of a clump in a coverage process where the first line segment of a clump has a distribution that differs from the remaining segments of the clump. This result allows us to provide the distribution of the busy period in an M/G/∞ queueing system with exceptional first service, and applications are considered. The result also provides the tool necessary to analyze the transient behavior of an ordinary coverage process, namely the depletion time of the ordinary M/G/∞ system.

Approximations for delays using asymptotic estimates

1984 ◽  
Vol 16 (01) ◽  
pp. 6
Author(s):  
David Y. Burman ◽  
Donald R. Smith
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Heavy Traffic ◽  
Single Server ◽  
Asymptotic Estimates ◽  
Single Server Queue ◽  
Average Delay ◽  
Multiserver Queues ◽  
Server Queue

Consider a general single-server queue where the customers arrive according to a Poisson process whose rate is modulated according to an independent Markov process. The authors have previously reported on limits for the average delay in light and heavy traffic. In this paper we review these results, extend them to multiserver queues, and describe some approximations obtained from them for general delays.

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