SINGLE SERVER QUEUES WITH A BATCH MARKOVIAN ARRIVAL PROCESS AND BULK RENEWAL OR NON-RENEWAL SERVICE

We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent o...

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Bibliographic Details
Published inJournal of systems science and systems engineering Vol. 24; no. 3; pp. 337 - 363
Main Author Banik, A. D.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2015
Springer Nature B.V
Subjects
Arrivals
Buffers
Complexity
Cost function
Economic Theory/Quantitative Economics/Mathematical Methods
Engineering
Operations Research/Decision Theory
Queuing theory
到达过程
平均等待时间
平均队列长度
服务器
服务时间
矩阵分析
长度分布
马尔可夫过程
matrix-analytic procedure
system-length distribution
cost control
infinite-buffer
Bulk service
rule
batch Markovian arrival process
,
cloud computing
queue
Markovian service process
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Summary:We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent of each other as well as the arrival process. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Next we obtain queue-length distributions at various other epochs such as, pre-arrival, arbitrary and pre-service using relations with post-departure epoch. Later we also obtain the system-length distributions at post-departure and arbitrary epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue-lengths and mean waiting times have been obtained Total expected cost function per trait time is also derived to determine the locally optimal values of a and b. Secondly, we perform similar analysis for the corresponding infinite-buffer single server queue where arrivals occur according to a BMAP and service process in this case follows a non-renewal one, namely, Markovian service process （MSP）.
Bibliography:11-2983/N
Bulk service （a, b）-rule, system-length distribution, infinite-buffer, queue, batch Markovian arrival process, Markovian service process, matrix-analytic procedure, cost control, cloud computing
We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent of each other as well as the arrival process. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Next we obtain queue-length distributions at various other epochs such as, pre-arrival, arbitrary and pre-service using relations with post-departure epoch. Later we also obtain the system-length distributions at post-departure and arbitrary epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue-lengths and mean waiting times have been obtained Total expected cost function per trait time is also derived to determine the locally optimal values of a and b. Secondly, we perform similar analysis for the corresponding infinite-buffer single server queue where arrivals occur according to a BMAP and service process in this case follows a non-renewal one, namely, Markovian service process （MSP）.
ISSN:1004-3756
1861-9576
DOI:10.1007/s11518-015-5268-y