Abstract
This paper investigates the steady state property of queue length for a batch arrival queue under N-policy with single vacation and setup times. When the system becomes empty, the server is turned off at once and takes a single vacation of random length . When he returns, if the queue length reaches or exceeds threshold , the server is immediately turned on but is temporarily unavailable due to a random setup time before offering service. If not, the server stays in the system until the queue length at least being . We derive the system size distribution and confirm the stochastic decomposition property. We also derive the recursion expressions of queue length distribution and other performance measures. Finally, we present some numerical examples to show the analytical results obtained. Sensitivity analysis is also performed.
Highlights
This paper investigates the steady state property of queue length for a batch arrival queue under N-policy with single vacation and setup times
This paper pays attention to a batch arrival queueing system under N-policy with a single vacation and setup times, which can model queue-like manufacturing/production/inventory system
We study the steady state queue length for an Mx/G/1 under N policy with single vacation and setup times
Summary
This paper pays attention to a batch arrival queueing system under N-policy with a single vacation and setup times, which can model queue-like manufacturing/production/inventory system. Lee et al [6,7] analyzed in detail a batch arrival Mx/G/1 queue under N-policy with a single vacation and repeated vacation respectively They derived the system size distribution which confirmed the famous stochastic decomposition property, and the optimal stationary operating policy was investigated. It is to be noted that few authors involved above considered the probability distribution of the number of customers in the system for batch arrival queue under N-policy with different vacations policies. Ke et al [17] used the maximum entropy solutions for batch arrival queue with an un-reliable server and delaying vacations They all derived the approximate formula for the probability distribution of the number of customers in the system. The effect of different system parameters on the queue length distribution is investigated
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