Due to unambiguous applications of bulk service vacation queues with set
up time in various fields such as pharmaceutical, aerospace engineering,
automobile industries etc., in this article, we analyze an
infinite-buffer batch-size-dependent bulk service queue with single and
multiple vacations, N-policy and set up time.
Customers/packets/units are served by a single server according to
general bulk service ( a,b) rule. The service time of a batch
dynamically vary with the batch-size and follows the general type of
distribution which covers a large scale of distributions. Firstly, we
generate the steady-state system equations. The main intend of this
study is to obtain the complete joint distribution of queue-length and
server content at service completion epoch, for which the bivariate
probability generating function has been derived. We extract the joint
distribution which is presented in a quite simple form and using those
we find the joint distribution at arbitrary epoch beside some marginal
distributions and performance measures. Finally, several numerical
examples along with graphical sketches have been provided to verify the
analytical results and to provide inner feeling to the system designers.
Discrete-time queueing system has widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze an infinite-buffer discrete-time group-arrival queue with single and multiple vacation policy where processing/transmission/service times dynamically vary with batch-size under service.The bivariate probability generating function of queue length and server content distribution has been derived first, and from that we extract the probabilities in terms of roots of the characteristic equation. We also find the joint distribution at arbitrary and pre-arrival slot. Discrete phase type distribution plays a noteworthy role in order to regulate the high transmission error through a particular channel. In view of this, numerical illustrations include the service time distribution to follow the discrete phase type distribution.
Queueing systems with bulk-service and vacation policy have become one of the pivotal interest for the researchers due to their widespread application in food processing technology, manufacturing systems etc. This article analyzes a single server versatile bulk-service queueing system wherein the customers arrive according to compound Poisson process and service time is dependent on the batch-size of undergoing service. Moreover, single and multiple vacation policy have been incorporated along with queue-length dependent vacation. After providing the steady-state system equations, the bivariate probability generating function of queue and server content distribution together has been derived at departure epoch. After the evaluation of the unknown probabilities , complete joint distribution has been extracted in terms of roots of the denominator of the bivariate pgf. The joint distribution at arbitrary epoch have also been reported. The discussed procedure and the reported results have been depicted through some numerical examples for different service and vacation time distributions. Some significant observation about the model have been sketched graphically.MSC Classification: 60G05 , 60K25
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