zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the batch arrival batch service queue with finite buffer under server’s vacation: MX/GY/1/N queue. (English) Zbl 1165.90407
Summary: We consider a finite-buffer batch arrival and batch service queue with single and multiple vacations. The steady-state distributions of the number of customers in the queue at service completion, vacation termination, departure, arbitrary and pre-arrival epochs have been obtained. Finally, various performance measures such as average queue length, average waiting time, probability that the server is busy, blocking probabilities, etc. are discussed along with some numerical results. The effect of certain model parameters on the key performance measures have also been investigated. The model has potential application in several areas including manufacturing, internet web-server and telecommunication systems.
MSC:
90B22Queues and service (optimization)
References:
[1]Chaudhry, M. L.; Templeton, J. G. C.: A first course in bulk queues, (1983) · Zbl 0559.60073
[2]Chang, S. H.; Choi, D. W.; Kim, T. S.: Performance analysis of a finite buffer bulk arrival and bulk service queue with variable server capacity, Stochastic analysis and applications 22, 1151-1173 (2004) · Zbl 1062.60094 · doi:10.1081/SAP-200026427
[3]Chang, S. H.; Choi, D. W.: Modeling and performance analysis of a finite buffer queue with batch arrivals, batch services and setup times: the MX/GY/1/K+B queue with setup times, INFORMS journal on computing 18, 218-228 (2006)
[4]Doshi, B. T.: Queueing systems with vacations – A survey, Queueing systems 1, 29-66 (1986) · Zbl 0655.60089 · doi:10.1007/BF01149327
[5]Takagi, H.: Queueing analysis – A foundation of performance evaluation, vacation and priority systems, Queueing analysis – A foundation of performance evaluation, vacation and priority systems 1 (1991) · Zbl 0744.60114
[6]Takagi, H.: Queueing analysis: A foundation of performance evaluation, finite systems, Queueing analysis: A foundation of performance evaluation, finite systems 2 (1993)
[7]Tian, N.; Zhang, Z. G.: Vacation queueing models–theory and applications, (2006)
[8]Baba, Y.: On the MX/G/1 queue with vacation time, Operations research letters 5, 93-98 (1986) · Zbl 0595.60094 · doi:10.1016/0167-6377(86)90110-0
[9]Dshalalow, J. H.; Yellen, J.: Bulk input queues with quorum and multiple vacations, Mathematical problems in engineering. Theory, methods, and applications 38, 707-721 (2001)
[10]Lee, H. W.; Lee, S. S.; Chae, K. C.; Nadarajan, R.: On a batch service queue with single vacation, Applied mathematical modelling 16, 36-42 (1992) · Zbl 0752.60081 · doi:10.1016/0307-904X(92)90113-H
[11]Lee, H. W.; Lee, S. S.; Chae, K. C.: A fixed-size batch service queue with vacations, Journal of applied mathematics and stochastic analysis 9, 205-219 (1996) · Zbl 0858.60085 · doi:10.1155/S1048953396000196
[12]Sikdar, K.; Gupta, U. C.: Analytic and numerical aspects of batch service queues with single vacation, Computers operations research 32, 943-966 (2005) · Zbl 1071.90016 · doi:10.1016/j.cor.2003.09.007
[13]Lee, T. T.: M/G/1/N queue with vacation time and exhaustive service discipline, Operations research 32, 774-784 (1984) · Zbl 0559.90032 · doi:10.1287/opre.32.4.774
[14]Frey, A.; Takahashi, Y.: A note on an M/GI/1/N queue with vacation time and exhaustive service discipline, Operations research letters 21, 95-100 (1997) · Zbl 0893.90065 · doi:10.1016/S0167-6377(97)00027-8
[15]Frey, A.; Takahashi, Y.: An MX/GI/1/N queue with closed-down and vacation times, Journal of applied mathematics and stochastic analysis 12, 63-83 (1999) · Zbl 0962.60088 · doi:10.1155/S1048953399000064
[16]Gupta, U. C.; Sikdar, K.: The finite-buffer M/G/1 queue with general bulk-service rule and single vacation, Performance evaluation 57, 199-219 (2004)
[17]Gupta, U. C.; Sikdar, K.: On the finite buffer bulk service M/G/1 queue with multiple vacations, Journal of probability and statistical science 3, 175-189 (2005)
[18]Grassmann, W. K.; Taksar, M. I.; Heyman, D. P.: Regenerative analysis and steady state distributions for Markov chains, Operations research 33, 1107-1116 (1985) · Zbl 0576.60083 · doi:10.1287/opre.33.5.1107
[19]M. Dümmler, Analysis of the departure process of the batch service queueing system, Research Report No.210, Institute of Computer Science, University of Würzburg, 1998