The infinite server queue and heuristic approximations to the multi-server queue with and without retrials

M. F. Ramalhoto

doi:10.1007/bf02564731

Fluid queue driven by a multi-server queue with multiple vacations and vacation interruption

RAIRO - Operations Research ◽

10.1051/ro/2017002 ◽

2017 ◽

Vol 51 (4) ◽

pp. 931-944

Author(s):

Senlin Yu ◽

Zaiming Liu ◽

Jinbiao Wu

Keyword(s):

Fluid Queue ◽

Multiple Vacations ◽

Server Queue ◽

Vacation Interruption ◽

Multi Server

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Analysis of Multi-Server Queue with Self-Sustained Servers

Mathematics ◽

10.3390/math9172134 ◽

2021 ◽

Vol 9 (17) ◽

pp. 2134

Author(s):

Alexander Dudin ◽

Olga Dudina ◽

Sergei Dudin ◽

Konstantin Samouylov

Keyword(s):

Three Dimensional ◽

Optimal Choice ◽

Arrival Process ◽

Queuing Model ◽

Numerical Result ◽

Self Sufficiency ◽

Server Queue ◽

Markov Arrival ◽

Markov Arrival Process ◽

Multi Server

A novel multi-server vacation queuing model is considered. The distinguishing feature of the model, compared to the standard queues, is the self-sufficiency of servers. A server can terminate service and go on vacation independently of the system manager and the overall situation in the system. The system manager can make decisions whether to allow the server to start work after vacation completion and when to try returning some server from a vacation to process customers. The arrival flow is defined by a general batch Markov arrival process. The problem of optimal choice of the total number of servers and the thresholds defining decisions of the manager arises. To solve this problem, the behavior of the system is described by the three-dimensional Markov chain with the special block structure of the generator. Conditions for the ergodicity of this chain are derived, the problem of computation of the steady-state distribution of the chain is discussed. Expressions for the key performance indicators of the system in terms of the distribution of the chain states are derived. An illustrative numerical result is presented.

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A Markov modulated multi-server queue with negative customers – The MM CPP/GE/c/L G-queue

Acta Informatica ◽

10.1007/pl00013307 ◽

2001 ◽

Vol 37 (11) ◽

pp. 881-919 ◽

Cited By ~ 25

Author(s):

Ram Chakka ◽

Peter G. Harrison

Keyword(s):

Negative Customers ◽

Server Queue ◽

Markov Modulated ◽

Multi Server

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Stationary Analysis of Infinite Server Queue with Batch Service

10.1007/978-3-030-91825-5_25 ◽

2021 ◽

pp. 411-424

Author(s):

Ayane Nakamura ◽

Tuan Phung-Duc

Keyword(s):

Batch Service ◽

Infinite Server ◽

Stationary Analysis ◽

Server Queue

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

Queueing Systems ◽

10.1007/s11134-008-9100-y ◽

2008 ◽

Vol 61 (1) ◽

pp. 65-84 ◽

Cited By ~ 26

Author(s):

Brian H. Fralix ◽

Ivo J. B. F. Adan

Keyword(s):

Markovian Environment ◽

Infinite Server ◽

Server Queue

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

Journal of Applied Probability ◽

10.2307/3214768 ◽

1993 ◽

Vol 30 (3) ◽

pp. 589-601 ◽

Cited By ~ 9

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.

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