Abstract
In this paper, we have a bulk arrival queueing Markovian model with two types of services first come first serve and bulk service. This model is also assumed the two servers such as main server and standby server with multiple vacations. If number of customers in the queue is less than ‘a’ then server will provide the FCFS service or goes for a vacation, if number of customers are more than or equal to ‘a’ then server will provide the bulk. After coming to the vacation, when the server will find number of customers are less than ‘a’ then he will provide the FCFS service to the customers. We have obtained the queue size distribution of this considered model and also obtained the performance measures such as idle time for the server, queue length, busy period by using the supplement variable technique.
Highlights
: In this paper, we have a bulk arrival queueing Markovian model with two types of services
Customers are served in batches according to the general individually and are served individually and in some bulk service rule in which, if there are less than ‘a’ customers models it is frequently observed that the customers arrive in in system server will not provide the batch service
We study a bulk arrival queueing system with first
Summary
Customers are served in batches according to the general individually and are served individually and in some bulk service rule in which, if there are less than ‘a’ customers models it is frequently observed that the customers arrive in in system server will not provide the batch service. Haridass and Arumuganathan (2008) examined the operating characteristics of an M X /G/1 queueing system with unreliable server and single They gave the probability generating function of the steady state system equations, expected number of customers in the system, expected length of busy period and idle period. Chen et al (2010) worked on the modified Markovian bulk-arrival and bulk-service queue with state-dependent control and studied the equilibrium behaviour They gave the results for the probability generating function of the equilibrium distribution, Queue length behavior. Parveen and Begum (2013) worked on a single server, bulk service queue with general arrival pattern and multiple working vacation They derived the steady state Probability distribution at pre arrival epoch and arbitrary epoch, mean queue length.
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