Browse > Article

Balking Phenomenon in the $M^{[x]}/G/1$ Vacation Queue  

Madan, Kailash C. (Department of Statistics, Yarmouk University)
Publication Information
Journal of the Korean Statistical Society / v.31, no.4, 2002 , pp. 491-507 More about this Journal
Abstract
We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.
Keywords
Compound Poisson arrival process; Bernoulli schedule server vacations; single vacation policy; balking; general service times; general vacation times; steady state;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Time dependent process of M/G/1 vacation models with exhaustive service /
[ Takagi, H. ] / Journal of Applied Probability   ScienceOn
2 Queueing systems with vacations a survey /
[ Doshi, B. T. ] / Queueing Systems
3 On a batch arrival Poisson queue with generalized vacation /
[ Borthakur, A.;Choudhury, G. ] / Sankhya
4 On the <TEX>$M^X$</TEX> /G/1 queue with vacation time /
[ Baba, Y. ] / Operations Research Letters   ScienceOn
5 A note on the M/G/1 queue with server vacations /
[ Fuhrman, S. ] / Operations Research
6 The <TEX>$M^X$</TEX> /G/1 queue with single and multiple vacations under LIFO service regime /
[ Rosenberg, E.;Yechiali, U. ] / Operations Research Letters   ScienceOn
7 Oscillating random walk models for GⅠ/G/1 vacation systems with Bernoulli schedules /
[ Keilson, J.;Servi, L. D. ] / Journal of Applied Probability   ScienceOn
8 Conditional and unconditional distributions for M/G/1 type queues with server vacation /
[ Doshi, B. T. ] / Queueing Systems
9 /
[ Takagi, H. ] / Queueing Analysis : A Foundation of Performance Evaluation
10 Analysis of <TEX>$M^X$</TEX> /G/1 queue with N-policy and multiple vacations /
[ Lee, H. W.;Lee, S. S.;Park, J. O.;Chae, K. C. ] / Journal of the Operational Research Society   ScienceOn
11 On a single server queue with two-stage heterogenous service and deterministic server vacations /
[ Madan, Kailash C. ] / International Journal of Systems Science   ScienceOn
12 The M/G/1 retrial queue with Bernoulli schedule /
[ Choi, B. D.;Park, K. K. ] / Queueing Systems
13 An <TEX>$M^X$</TEX> /G/1 queueing system with a set up period and a vacation period /
[ Choudhury, G. ] / Queueing Systems
14 Stationary distributions in a queueing system with vacation times and limited service /
[ Cramer, M. ] / Queueing Systems
15 Operating characteristics of <TEX>$M^X$</TEX> /G/1 queue with N-policy /
[ Lee, H. W.;Lee, S. S.;Chae, K. C. ] / Queueing Systems
16 An M/M/s queue with server's vacations /
[ Levi, Y.;Yechiali, U. ] / Information Systems and Operational Research
17 /
[ Medhi, J. ] / Stochastic Processes
18 <TEX>$M^X$</TEX> /G/1 vacation models with N-policy : Heuristic interpretation of the mean waiting time /
[ Chae, K. C.;Lee, H. W. ] / Journal of the Operational Research Society   ScienceOn
19 An M/G/1 queue with optional deterministic server vacations /
[ Madan, Kailash C. ] / Metron