scholarly journals Explicit solution for the stationary distribution of a discrete-time finite buffer queue

2015 ◽  
Vol 12 (3) ◽  
pp. 1121-1133 ◽  
Author(s):  
Bara Kim ◽  
Jeongsim Kim
Keyword(s):  
Stationary Distribution ◽  
Discrete Time ◽  
Explicit Solution ◽  
Finite Buffer ◽  
Finite Buffer Queue

Performance analysis of the discrete-time GI/Geom/1/N queue

1996 ◽  
Vol 33 (01) ◽  
pp. 239-255 ◽  
Author(s):  
M. L. Chaudhry ◽  
U. C. Gupta
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Interarrival Time ◽  
Single Server ◽  
Finite Buffer ◽  
Supplementary Variable ◽  
Time Analysis ◽  
Variable Technique ◽  
Early Arrival ◽  
Finite Buffer Queue

This paper presents an analysis of the single-server discrete-time finite-buffer queue with general interarrival and geometric service time,GI/Geom/1/N. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variations of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both cases, steady-state distributions for outside observers as well as at random and prearrival epochs have been obtained. The waiting time analysis has also been carried out. Results for theGeom/G/1/Nqueue with LAS-DA have been obtained from theGI/Geom/1/Nqueue with EAS. We also give various performance measures. An algorithm for computing state probabilities is given in an appendix.

Performance analysis of the discrete-time GI/Geom/1/N queue

1996 ◽  
Vol 33 (1) ◽  
pp. 239-255 ◽  
Author(s):  
M. L. Chaudhry ◽  
U. C. Gupta
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Interarrival Time ◽  
Single Server ◽  
Finite Buffer ◽  
Supplementary Variable ◽  
Time Analysis ◽  
Variable Technique ◽  
Early Arrival ◽  
Finite Buffer Queue

This paper presents an analysis of the single-server discrete-time finite-buffer queue with general interarrival and geometric service time, GI/Geom/1/N. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variations of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both cases, steady-state distributions for outside observers as well as at random and prearrival epochs have been obtained. The waiting time analysis has also been carried out. Results for the Geom/G/1/N queue with LAS-DA have been obtained from the GI/Geom/1/N queue with EAS. We also give various performance measures. An algorithm for computing state probabilities is given in an appendix.

scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

Discrete time analysis of a repairable machine

2002 ◽  
Vol 39 (3) ◽  
pp. 503-516 ◽  
Author(s):  
Attahiru Sule Alfa ◽  
I. T. Castro
Keyword(s):  
Detailed Analysis ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Single Machine ◽  
General Distribution ◽  
Optimal Time ◽  
Time Analysis ◽  
Machine System ◽  
Special Cases

We consider, in discrete time, a single machine system that operates for a period of time represented by a general distribution. This machine is subject to failures during operations and the occurrence of these failures depends on how many times the machine has previously failed. Some failures are repairable and the repair times may or may not depend on the number of times the machine was previously repaired. Repair times also have a general distribution. The operating times of the machine depend on how many times it has failed and was subjected to repairs. Secondly, when the machine experiences a nonrepairable failure, it is replaced by another machine. The replacement machine may be new or a refurbished one. After the Nth failure, the machine is automatically replaced with a new one. We present a detailed analysis of special cases of this system, and we obtain the stationary distribution of the system and the optimal time for replacing the machine with a new one.

AN EXPLICIT SOLUTION TO THE DISCRETE-TIME SINGULAR LQ REGULATION PROBLEM FOR NON-SQUARE PLANT

2005 ◽  
Vol 38 (1) ◽  
pp. 265-270
Author(s):  
Wataru Kase ◽  
Ryoji Miyoshi ◽  
Yasuhiko Mutoh
Keyword(s):  
Discrete Time ◽  
Explicit Solution

Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems

2014 ◽  
Vol 4 (4) ◽  
pp. 386-395
Author(s):  
Pei-Chang Guo
Keyword(s):  
Markov Chains ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Matrix Equation ◽  
Nonnegative Solution ◽  
Minimal Nonnegative Solution ◽  
The Minimal Nonnegative Solution ◽  
Quadratic Matrix Equation ◽  
Quadratic Matrix ◽  
Birth Death

AbstractIn order to determine the stationary distribution for discrete time quasi-birth-death Markov chains, it is necessary to find the minimal nonnegative solution of a quadratic matrix equation. The Newton-Shamanskii method is applied to solve this equation, and the sequence of matrices produced is monotonically increasing and converges to its minimal nonnegative solution. Numerical results illustrate the effectiveness of this procedure.

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