Transient Analysis of X M /G(a,b)/1 queueing system with
Balking under Bernoulli Schedule Vacation and
Random Breakdown

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

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Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations

Journal of Systems Science and Information ◽

10.21078/jssi-2018-069-16 ◽

2018 ◽

Vol 6 (1) ◽

pp. 69-84

Author(s):

Jia Xu ◽

Liwei Liu ◽

Taozeng Zhu

Keyword(s):

Generating Functions ◽

Transient Analysis ◽

Bessel Functions ◽

Queueing System ◽

System Size ◽

Heterogeneous Servers ◽

Modified Bessel Functions ◽

Multiple Vacations ◽

Special Cases ◽

Mean And Variance

AbstractWe consider anM/M/2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities, mean and variance of the system size at timetby employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

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Transient analysis of queueing system with two heterogeneous servers

Journal of Physics Conference Series ◽

10.1088/1742-6596/1333/3/032039 ◽

2019 ◽

Vol 1333 ◽

pp. 032039

Author(s):

L I Korolkova ◽

N Mashrabov ◽

A M Murzin ◽

A V Panfilov ◽

Ju L Siuskina

Keyword(s):

Transient Analysis ◽

Queueing System ◽

Heterogeneous Servers

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Transient analysis of the M/M/1 queue

Advances in Applied Probability ◽

10.1017/s0001867800025623 ◽

1993 ◽

Vol 25 (03) ◽

pp. 702-713 ◽

Cited By ~ 8

Author(s):

P. Leguesdron ◽

J. Pellaumail ◽

G. Rubino ◽

B. Sericola

Keyword(s):

Markov Chain ◽

Generating Function ◽

Transient Analysis ◽

Queueing System ◽

Second Step ◽

New Approach ◽

Analytical Expression ◽

Transient Probabilities

A new approach is used to obtain the transient probabilities of the M/M/1 queueing system. The first step of this approach deals with the generating function of the transient probabilities of the uniformized Markov chain associated with this queue. The second step consists of the inversion of this generating function. A new analytical expression of the transient probabilities of the M/M/1 queue is then obtained.

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