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Heterogeneous Servers Markov Queue with Single and Batch Service

https://doi.org/10.51514/JSTR.2.4.2020.25-30

K.P.S. Baghel* and M. Jain

ABSTRACT

The paper addresses the Markovian queueing problem for stochastic environments wherein repair jobs of failed machines arrive according to FCFS order. The repair facility consists of two heterogeneous repairmen who facilitate the repair of the failed machines with different repair rates. In case if the queue size is less than or equal to a control    limit ‘L’, each failed machine is repaired by the both servers with effective at rates m= m1 + m2  , where m1 > m2 .When the queue size becomes greater than L and less than K, the machines are recovered with a faster rate mf. If the size of  queue exceeds K, all the machines are repaired together in a batch at rate mb. To determine the steady-state probabilities and other key performance indices, a recursive technique is applied. To find the optimal value of the threshold parameter K, a cost function is also facilitated. The effects of system descriptors on the performance indices are visually depicted by graphs.

Keywords: Markov, FCFS, Single and Batch service, Heterogeneous servers, Steady state, Recursive  Technique, Cost Function.