Genetic Cost Optimization of the GI/M/1/N Finite-Buffer Queue with a Single Vacation Policy

2013 ◽  
pp. 12-23 ◽  
Author(s):  
Marcin Gabryel ◽  
Robert K. Nowicki ◽  
Marcin Woźniak ◽  
Wojciech M. Kempa
Keyword(s):  
Cost Optimization ◽  
Finite Buffer ◽  
Single Vacation ◽  
Finite Buffer Queue

scholarly journals A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

2014 ◽  
Vol 24 (4) ◽  
pp. 887-900 ◽  
Author(s):  
Marcin Woźniak ◽  
Wojciech M. Kempa ◽  
Marcin Gabryel ◽  
Robert K. Nowicki
Keyword(s):  
Busy Period ◽  
Optimization Problem ◽  
Analytical Study ◽  
Cost Optimization ◽  
Queueing Systems ◽  
Evolutionary Strategy ◽  
Finite Buffer ◽  
Single Vacation ◽  
Erlang Distributions ◽  
Finite Buffer Queue

Abstract In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

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.

scholarly journals Aspects of Impatience in a Finite Buffer Queue

2012 ◽  
Vol 46 (3) ◽  
pp. 189-209
Author(s):  
Medhi Pallabi ◽  
Amit Choudhury
Keyword(s):  
Finite Buffer ◽  
Finite Buffer Queue

ADMISSION CONTROL WITH INCOMPLETE INFORMATION TO A FINITE BUFFER QUEUE

2006 ◽  
Vol 21 (1) ◽  
pp. 19-46 ◽  
Author(s):  
Dorothée Honhon ◽  
Sridhar Seshadri
Keyword(s):  
Admission Control ◽  
Partial Information ◽  
Control Policy ◽  
Arrival Process ◽  
Finite Buffer ◽  
Optimal Cost ◽  
State Aggregation ◽  
The Cost ◽  
Finite Buffer Queue

We consider the problem of admission control to a multiserver finite buffer queue under partial information. The controller cannot see the queue but is informed immediately if an admitted customer is lost due to buffer overflow. Turning away (i.e., blocking) customers is costly and so is losing an admitted customer. The latter cost is greater than that of blocking. The controller's objective is to minimize the average cost of blocking and rejection per incoming customer. Lin and Ross [11] studied this problem for multiserver loss systems. We extend their work by allowing a finite buffer and the arrival process to be of the renewal type. We propose a control policy based on a novel state aggregation approach that exploits the regenerative structure of the system, performs well, and gives a lower bound on the optimal cost. The control policy is inspired by a simulation technique that reduces the variance of the estimators by not simulating the customer service process. Numerical experiments show that our bound varies with the load offered to the system and is typically within 1% and 10% of the optimal cost. Also, our bound is tight in the important case when the cost of blocking is low compared to the cost of rejection and the load offered to the system is high. The quality of the bound degrades with the degree of state aggregation, but the computational effort is comparatively small. Moreover, the control policies that we obtain perform better compared to a heuristic suggested by Lin and Ross. The state aggregation technique developed in this article can be used more generally to solve problems in which the objective is to control the time to the end of a cycle and the quality of the information available to the controller degrades with the length of the cycle.

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