scholarly journals Steady-state characteristics of three-channel queueing systems with Erlangian service times

2016 ◽  
Vol 15 (3) ◽  
pp. 75-87
Author(s):  
Bohdan Kopytko ◽  
◽  
Kostyantyn Zhernovyi ◽  
Keyword(s):  
Steady State ◽  
Queueing Systems ◽  
Erlangian Service Times ◽  
Service Times

scholarly journals M/M/1 Multiple Vacation Queueing Systems with Differentiated Vacations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Oliver C. Ibe ◽  
Olubukola A. Isijola
Keyword(s):  
Steady State ◽  
Busy Period ◽  
Queueing System ◽  
Queueing Systems ◽  
Steady State Solution ◽  
State Solution ◽  
Multiple Vacation ◽  
Service Times

We consider a multiple vacation queueing system in which a vacation following a busy period has a different distribution from a vacation that is taken without serving at least one customer. For ease of analysis it is assumed that the service times are exponentially distributed and the two vacation types are also exponentially distributed but with different means. The steady-state solution is obtained.

scholarly journals Multipreconditioned GMRES for simulating stochastic automata networks

2018 ◽  
Vol 16 (1) ◽  
pp. 986-998
Author(s):  
Chun Wen ◽  
Ting-Zhu Huang ◽  
Xian-Ming Gu ◽  
Zhao-Li Shen ◽  
Hong-Fan Zhang ◽  
...  
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Linear Systems ◽  
Iterative Methods ◽  
Communication Systems ◽  
Queueing Systems ◽  
Steady State Probability ◽  
Stochastic Automata ◽  
Automata Networks ◽  
Generator Matrices

AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

The steady-state distribution of spent service times present in the M/G/1 foreground–background processor-sharing queue

1988 ◽  
Vol 25 (1) ◽  
pp. 194-203 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Steady State ◽  
Random Measure ◽  
Processor Sharing ◽  
Steady State Distribution ◽  
State Distribution ◽  
Generating Functional ◽  
Service Times

The steady-state distribution of spent service times present in the M/G/1 foreground-background processor-sharing queue is described by a random measure, whose generating functional is obtained.

On a tandem queueing model with identical service times at both counters, II

1979 ◽  
Vol 11 (3) ◽  
pp. 644-659 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Heavy Traffic ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
In Series ◽  
Mean And Variance ◽  
Queues In Series ◽  
The Mean ◽  
Service Times ◽  
Practical Implications

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

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