On the average idle time and average queue length estimates in an M/M/1 queue

  • Authors:

  • Anurag Kumar

  • Affiliations:

  • Dept. of Electrical Communication Engineering, Indian Institute of Science, Bangalore, 560 012, India

  • Venue:
  • Operations Research Letters
  • Year:
  • 1992

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Abstract

We study the bias in the means of average idle time and average queue length estimates, over the interval [0, t], in a transient M/M/1 queue. We develop some formulas, in terms of the busy period distribution, that show that the bias is O(1t). These formulas yield simple bounds for the means of the transient estimates. The bound for the bias in the mean of the average idle time estimate is also shown to be an excellent approximation.