Transient solutions for denumerable-state Markov processes

1994 ◽  
Vol 31 (3) ◽  
pp. 635-645 ◽  
Author(s):  
Guang-Hui Hsu ◽  
Xue-Ming Yuan
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Initial Distribution ◽  
Numerical Results ◽  
Transient Solution ◽  
Queue Length Distribution ◽  
Transient Solutions

The algorithm for the transient solution for the denumerable state Markov process with an arbitrary initial distribution is given in this paper. The transient queue length distribution for a general Markovian queueing system can be obtained by this algorithm. As examples, some numerical results are presented.

Transient solutions for denumerable-state Markov processes

1994 ◽  
Vol 31 (03) ◽  
pp. 635-645
Author(s):  
Guang-Hui Hsu ◽  
Xue-Ming Yuan
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Initial Distribution ◽  
Numerical Results ◽  
Transient Solution ◽  
Queue Length Distribution ◽  
Transient Solutions

The algorithm for the transient solution for the denumerable state Markov process with an arbitrary initial distribution is given in this paper. The transient queue length distribution for a general Markovian queueing system can be obtained by this algorithm. As examples, some numerical results are presented.

A non-exponential queueing system with independent arrivals and batch servicing

1990 ◽  
Vol 27 (02) ◽  
pp. 401-408
Author(s):  
Nico M. Van Dijk ◽  
Eric Smeitink
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Service Systems ◽  
Batch Service ◽  
Repair System ◽  
Theoretical Interest ◽  
Form Expression ◽  
Queue Length Distribution ◽  
Service Times

We study a queueing system with a finite number of input sources. Jobs are individually generated by a source but wait to be served in batches, during which the input of that source is stopped. The service speed of a server depends on the mode of other sources and thus includes interdependencies. The input and service times are allowed to be generally distributed. A classical example is a machine repair system where the machines are subject to shocks causing cumulative damage. A product-form expression is obtained for the steady state joint queue length distribution and shown to be insensitive (i.e. to depend on only mean input and service times). The result is of both practical and theoretical interest as an extension of more standard batch service systems.

Relationships and decomposition in the delayed bernoulli feedback queueing system

1988 ◽  
Vol 25 (1) ◽  
pp. 169-183 ◽  
Author(s):  
D. König ◽  
M. Miyazawa
Keyword(s):  
Generating Function ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Arrival Process ◽  
Stieltjes Transform ◽  
Bernoulli Feedback ◽  
Queue Length Distribution ◽  
Workload Distribution ◽  
Feedback Queue

For the delayed Bernoulli feedback queue with first come–first served discipline under weak assumptions a relationship for the generating functions of the joint queue-length distribution at various points in time is given. A decomposition for the generating function of the stationary total queue length distribution has been proven. The Laplace-Stieltjes transform of the stationary joint workload distribution function is represented by its marginal distributions. The arrival process is Poisson, renewal or arbitrary stationary, respectively. The service times can form an i.i.d. sequence at each queue. Different kinds of product form of the generating function of the joint queue-length distribution are discussed.

On a non-Markovian time-dependent queueing system

1989 ◽  
Vol 26 (1) ◽  
pp. 142-151 ◽  
Author(s):  
S. D. Sharma
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Transient State ◽  
Time Dependent ◽  
Queue Length Distribution ◽  
State Behaviour

This paper studies the transient and steady-state behaviour of a continuous and discrete-time queueing system with non-Markovian type of departure mechanism. The Laplace transforms of the probability generating function of the time-dependent queue length distribution in the transient state are obtained and the probability generating function of the queue length distribution in the steady state is derived therefrom. Finally, some particular cases are discussed.

scholarly journals Asymptotic analysis of a queueing system by a two-dimensional state space

1984 ◽  
Vol 21 (4) ◽  
pp. 870-886 ◽  
Author(s):  
J. P. C. Blanc
Keyword(s):  
Asymptotic Analysis ◽  
Queue Length ◽  
Queueing System ◽  
Queueing Systems ◽  
Length Distribution ◽  
Time Dependent ◽  
Queue Length Distribution ◽  
Long Run ◽  
Dimensional State Space ◽  
Hilbert Type

A technique is developed for the analysis of the asymptotic behaviour in the long run of queueing systems with two waiting lines. The generating function of the time-dependent joint queue-length distribution is obtained with the aid of the theory of boundary value problems of the Riemann–Hilbert type and by introducing a conformal mapping of the unit disk onto a given domain. In the asymptotic analysis an extensive use is made of theorems on the boundary behaviour of such conformal mappings.

scholarly journals DELAY IN A TANDEM QUEUEING MODEL WITH MOBILE QUEUES: AN ANALYTICAL APPROXIMATION

2014 ◽  
Vol 28 (3) ◽  
pp. 363-387 ◽  
Author(s):  
Ahmad Al Hanbali ◽  
Roland de Haan ◽  
Richard J. Boucherie ◽  
Jan-Kees van Ommeren
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Analytical Approximation ◽  
Traffic Load ◽  
Light Traffic ◽  
Delay Performance ◽  
Queue Length Distribution ◽  
End To End Delay ◽  
Length Analysis

In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on queue-length analysis. Through extensive numerical validation, we find that the queue-length approximation exhibits excellent performance for light traffic load.

scholarly journals Asymptotic analysis of a queueing system by a two-dimensional state space

1984 ◽  
Vol 21 (04) ◽  
pp. 870-886
Author(s):  
J. P. C. Blanc
Keyword(s):  
Asymptotic Analysis ◽  
Queue Length ◽  
Queueing System ◽  
Queueing Systems ◽  
Length Distribution ◽  
Time Dependent ◽  
Queue Length Distribution ◽  
Long Run ◽  
Dimensional State Space ◽  
Hilbert Type

A technique is developed for the analysis of the asymptotic behaviour in the long run of queueing systems with two waiting lines. The generating function of the time-dependent joint queue-length distribution is obtained with the aid of the theory of boundary value problems of the Riemann–Hilbert type and by introducing a conformal mapping of the unit disk onto a given domain. In the asymptotic analysis an extensive use is made of theorems on the boundary behaviour of such conformal mappings.

On a non-Markovian time-dependent queueing system

1989 ◽  
Vol 26 (01) ◽  
pp. 142-151
Author(s):  
S. D. Sharma
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Transient State ◽  
Time Dependent ◽  
Queue Length Distribution ◽  
State Behaviour

This paper studies the transient and steady-state behaviour of a continuous and discrete-time queueing system with non-Markovian type of departure mechanism. The Laplace transforms of the probability generating function of the time-dependent queue length distribution in the transient state are obtained and the probability generating function of the queue length distribution in the steady state is derived therefrom. Finally, some particular cases are discussed.

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