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Title: Performance prediction of loss and delay Markovian queueing model with nopassing and removable additional servers
Authors: Jain M.
Singh P.
Published in: Computers and Operations Research
Abstract: In this investigation, the loss and delay Markovian queueing system with nopassing is proposed. The customers may balk or renege with certain probability, on finding all servers busy on their arrival. To cope up with the balking and reneging behaviour of the customers, there is provision of removable additional servers apart from permanent servers so as to provide the better grade of service at optimal cost operating conditions. The customers are classified into two classes depending upon whether they can wait or lost when all servers are busy. The customers can also be categorized into two classes from service point of view. Type A customers have zero service time whereas type B customers have exponential service time. The explicit expressions for the average number of customers in the system, the expected waiting time for both types of customers, etc., are derived by using steady-state queue size distribution. Some earlier results are deduced by setting appropriate system parameters. The system behaviour is examined with the help of numerical illustrations by varying different parameters. The performance prediction of various systems in communication switching network, remote border security check post, jobs processing in computers, etc., are influenced by the customers behaviour, in particular, when nopassing constraints are prevalent. The incorporation of loss and delay phenomena is likely to bring about understanding whether the customers would like to wait in the queue or would be lost in case when all servers are busy. The provision of additional removable servers will be helpful in upgrading the service and to reduce the discouragement behaviour of the customers in such congestion situations. © 2002 Elsevier Science Ltd. All rights reserved.
Citation: Computers and Operations Research (2003), 30(8): 1233-1253
Issue Date: 2003
Keywords: Balking
Expected waiting time
Loss and delay
Removable additional servers
ISSN: 3050548
Author Scopus IDs: 7402070856
Author Affiliations: Jain, M., School of Mathematical Sciences, Institute of Basic Science, Khandari, Agra 282002, India
Singh, P., School of Mathematical Sciences, Institute of Basic Science, Khandari, Agra 282002, India
Funding Details: The authors are thankful to University Grants Commission New Delhi vide project no. 8-5/98 (SR-I) for providing financial assistance to carry out this research work. The authors are also indebted to the learned referees and the editors for their constructive comments and suggestions, which improved the presentation of the paper considerably. Appendix The cumulative distribution function (c.d.f.) of service times for a tagged customer is given by F(x)=(1−p)+p(1− x⩾0, 0<p⩽1. exp (−μ n x) for The expressions for the mean waiting time of types A and B customers are given by (A.1) E(W A )= 1 μ a ∑ n=0 s n + ∑ n=s+1 K +a n−s+1 s s−1 + ∑ j=1 r−1 ∑ n=jK+1 (j+1)K +a n−(s+j)+1 (s+j) s+j−1 + ∑ n=rK+1 L +a n−(s+r)+1 (s+r) s+r P n , and (A.2) E(W B )= 1 μ a ∑ n=0 s n+1 + ∑ n=s+1 K +a n−s+1 s s + ∑ j=1 r−1 ∑ n=jK+1 (j+1)K +a n−(s+j)+1 (s+j) s+j + ∑ n=rK+1 L +a n−(s+r)+1 (s+r) s+r P n , where L takes the value N and M in case of FCM and FPM models, respectively. We also have (A.3) a n = 0 n=0, 1/i ∑ i=1 n n=1,2,…,n.
Corresponding Author: Jain, M.; School of Mathematical Sciences, Institute of Basic Science, Khandari, Agra 282002, India; email:
Appears in Collections:Journal Publications [MA]

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