The Ergodic Queue Length Distribution for Queueing Systems with Finite Capacity

1966 ◽  
Vol 28 (1) ◽  
pp. 190-201 ◽  
Author(s):  
J. Keilson
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Length Distribution ◽  
Finite Capacity ◽  
Queue Length Distribution

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 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 single server queue with negative arrivals and request repeated

1999 ◽  
Vol 36 (3) ◽  
pp. 907-918 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Gomez-Corral
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Length Distribution ◽  
Single Server ◽  
System State ◽  
Single Server Queue ◽  
Queue Length Distribution ◽  
Server Queue ◽  
Regenerative Approach ◽  
Negative Arrivals

There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.

Analytical solution of finite capacity M/D/1 queues

2000 ◽  
Vol 37 (04) ◽  
pp. 1092-1098
Author(s):  
Olivier Brun ◽  
Jean-Marie Garcia
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Point Of View ◽  
Queueing Model ◽  
Finite Capacity ◽  
Computational Point ◽  
Queue Length Distribution ◽  
The Mean ◽  
Mean Queue Length ◽  
Number Of Customers

Although the M/D/1/N queueing model is well solved from a computational point of view, there is no known analytical expression of the queue length distribution. In this paper, we derive closed-form formulae for the distribution of the number of customers in the system in the finite-capacity M/D/1 queue. We also give an explicit solution for the mean queue length and the average waiting time.

On a single server queue with negative arrivals and request repeated

1999 ◽  
Vol 36 (03) ◽  
pp. 907-918 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Gomez-Corral
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Length Distribution ◽  
Single Server ◽  
System State ◽  
Single Server Queue ◽  
Queue Length Distribution ◽  
Server Queue ◽  
Regenerative Approach ◽  
Negative Arrivals

There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.

Analytical solution of finite capacity M/D/1 queues

2000 ◽  
Vol 37 (4) ◽  
pp. 1092-1098 ◽  
Author(s):  
Olivier Brun ◽  
Jean-Marie Garcia
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Point Of View ◽  
Queueing Model ◽  
Finite Capacity ◽  
Computational Point ◽  
Queue Length Distribution ◽  
The Mean ◽  
Mean Queue Length ◽  
Number Of Customers

Although the M/D/1/N queueing model is well solved from a computational point of view, there is no known analytical expression of the queue length distribution. In this paper, we derive closed-form formulae for the distribution of the number of customers in the system in the finite-capacity M/D/1 queue. We also give an explicit solution for the mean queue length and the average waiting time.

Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N, D)-Policy

2020 ◽  
Vol 8 (4) ◽  
pp. 367-386
Author(s):  
Yingyuan Wei ◽  
Yinghui Tang ◽  
Miaomiao Yu
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Length Distribution ◽  
Transient State ◽  
Total Probability ◽  
Initial State ◽  
Queue Length Distribution ◽  
Recursive Solution ◽  
Arbitrary Initial State ◽  
Capacity Decision

AbstractIn this paper we consider a discrete-time Geo/G/1 queue with delayed Min(N, D)-policy. Using renewal process theory, total probability decomposition technique and z-transform, we study the transient and equilibrium properties of the queue length from an arbitrary initial state, and obtain both the recursive expressions of the transient state queue length distribution and the steady state queue length distribution at arbitrary time epoch n+. Furthermore, we derive the important relations between equilibrium queue length distributions at different time epochs n–, n and n+. Finally, we give some numerical examples about capacity decision in queueing systems to demonstrate the application of the analytical results reported in this paper.

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