An Approximation to the Overshoot in M/En/1 Queues

M/En/1 큐에서 Overshoot에 대한 근사

Bae, Jong-Ho;Jeong, Ah-Reum;Kim, Sung-Gon

  • Received : 20100800
  • Accepted : 20101100
  • Published : 2011.04.30


In this paper, we propose an approximation to the overshoot in M/$E_n$/1 queues. Overshoot means the size of excess over the threshold when the workload process of an M/$E_n$/1 queue exceeds a prespecified threshold. The distribution, $1^{st}$ and $2^{nd}$ moments of overshoot have an important role in solving some kind of optimization problems. For the approximation to the overshoot, we propose a formula that is a convex sum of the service time distribution and an exponential distribution. We also do a numerical study to check how exactly the proposed formula approximates the overshoot.


M/$E_n$/1 queue;overshoot;approximation


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