Multi-server Queue with Job Service Time Depending on a Background Process

2016 ◽  
pp. 163-171 ◽  
Author(s):  
Tomoyuki Sakata ◽  
Shoji Kasahara
Keyword(s):  
Service Time ◽  
Background Process ◽  
Server Queue ◽  
Multi Server

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

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

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

scholarly journals Analysis of Multi-Server Queue with Self-Sustained Servers

Mathematics ◽  
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.

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

2001 ◽  
Vol 37 (11) ◽  
pp. 881-919 ◽  
Author(s):  
Ram Chakka ◽  
Peter G. Harrison
Keyword(s):  
Negative Customers ◽  
Server Queue ◽  
Markov Modulated ◽  
Multi Server

Analysis of an infinite multi-server queue with an optional service

2013 ◽  
Vol 65 (2) ◽  
pp. 216-225 ◽  
Author(s):  
Jau-Chuan Ke ◽  
Chia-Huang Wu ◽  
Wen Lea Pearn
Keyword(s):  
Optional Service ◽  
Server Queue ◽  
Multi Server

A note on the queueing systems GI/D/1 and D/G/1

1970 ◽  
Vol 7 (2) ◽  
pp. 465-468 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Service Time ◽  
Special Form ◽  
Arrival Time ◽  
Queueing Systems ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue ◽  
Image Position ◽  
The Right ◽  
Similar Evaluation

In this note we adopt the notation and terminology of Kingman (1966) without further comment. For the general single server queue one has For the queueing systems GI/D/1 and D/G/1 we shall show that it is possible to make use of the special form of the service time and inter-arrival time distributions, respectively, to evaluate the right hand side of (1). A similar evaluation applies to the limiting distribution when it exists. The results obtained could also be obtained from those of Finch (1969) and Henderson and Finch (1970) by using suitable limiting arguments.

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