scholarly journals An LCFS finite buffer model with finite source batch input

1989 ◽  
Vol 26 (02) ◽  
pp. 372-380
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Queueing Systems ◽  
Length Distribution ◽  
Source Distribution ◽  
Closed Form Expression ◽  
Finite Buffer ◽  
Form Expression ◽  
Batch Arrivals ◽  
Queue Length Distribution ◽  
Recursive Computation ◽  
Batch Input

Queueing systems are studied with a last-come, first-served queueing discipline and batch arrivals generated by a finite number of non-exponential sources. A closed-form expression is derived for the steady-state queue length distribution. This expression has a scaled geometric form and is insensitive to the input distribution. Moreover, an algorithm for the recursive computation of the normalizing constant and the busy source distribution is presented. The results are of both practical and theoretical interest as an extension of the standard Poisson batch input case.

scholarly journals An LCFS finite buffer model with finite source batch input

1989 ◽  
Vol 26 (2) ◽  
pp. 372-380 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Queueing Systems ◽  
Length Distribution ◽  
Source Distribution ◽  
Closed Form Expression ◽  
Finite Buffer ◽  
Form Expression ◽  
Batch Arrivals ◽  
Queue Length Distribution ◽  
Recursive Computation ◽  
Batch Input

Queueing systems are studied with a last-come, first-served queueing discipline and batch arrivals generated by a finite number of non-exponential sources. A closed-form expression is derived for the steady-state queue length distribution. This expression has a scaled geometric form and is insensitive to the input distribution. Moreover, an algorithm for the recursive computation of the normalizing constant and the busy source distribution is presented. The results are of both practical and theoretical interest as an extension of the standard Poisson batch input case.

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (01) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also 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.

Infinite- and finite-buffer Markov fluid queues: a unified analysis

2004 ◽  
Vol 41 (02) ◽  
pp. 557-569 ◽  
Author(s):  
Nail Akar ◽  
Khosrow Sohraby
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Length Distribution ◽  
Matrix Exponential ◽  
Divide And Conquer ◽  
Buffer System ◽  
Finite Buffer ◽  
Fluid Queues ◽  
Queue Length Distribution ◽  
Markov Fluid Queues

In this paper, we study Markov fluid queues where the net fluid rate to a single-buffer system varies with respect to the state of an underlying continuous-time Markov chain. We present a novel algorithmic approach to solve numerically for the steady-state solution of such queues. Using this approach, both infinite- and finite-buffer cases are studied. We show that the solution of the infinite-buffer case is reduced to the solution of a generalized spectral divide-and-conquer (SDC) problem applied on a certain matrix pencil. Moreover, this SDC problem does not require the individual computation of any eigenvalues and eigenvectors. Via the solution for the SDC problem, a matrix-exponential representation for the steady-state queue-length distribution is obtained. The finite-buffer case, on the other hand, requires a similar but different decomposition, the so-called additive decomposition (AD). Using the AD, we obtain a modified matrix-exponential representation for the steady-state queue-length distribution. The proposed approach for the finite-buffer case is shown not to have the numerical stability problems reported in the literature.

scholarly journals On the value function of the M/Cox(r)/1 queue

2006 ◽  
Vol 43 (2) ◽  
pp. 363-376 ◽  
Author(s):  
Sandjai Bhulai
Keyword(s):  
Value Function ◽  
Queueing Systems ◽  
Single Step ◽  
Closed Form Expression ◽  
Single Server ◽  
Form Expression ◽  
Coxian Distribution ◽  
Optimal Value ◽  
Service Times ◽  
The Value Function

We consider a single-server queueing system at which customers arrive according to a Poisson process. The service times of the customers are independent and follow a Coxian distribution of order r. The system is subject to costs per unit time for holding a customer in the system. We give a closed-form expression for the average cost and the corresponding value function. The result can be used to derive nearly optimal policies in controlled queueing systems in which the service times are not necessarily Markovian, by performing a single step of policy iteration. We illustrate this in the model where a controller has to route to several single-server queues. Numerical experiments show that the improved policy has a close-to-optimal value.

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.

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (1) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

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