Recursive Formula for the Moments of Queue Length in the M/M/1 Queue

Jianming Liu · Xiaohong Jiang · S. Horiguchi

11 citations0/0 files storedIEEE Communications Letters

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Age of Information Optimization

Abstract

This letter presents the recursive formulas of the moments of queue length for the M/M/1 queue and M/M/1/B queue, respectively. The higher moments of queue length are important for optimization problem. Our method provides an alternative approach to derive the moments of queue length, instead of taking the derivatives of the moment generating function.

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References

1994Stochastic Models in Queueing Theory.2003Stochastic Models in Queueing Theory 1993Analysis of packet loss processes in high-speed networks 1989Calculating time-dependent performance measures for the M/M/1 queue 1998Loss probabilities for messages with redundant packets feeding a finite buffer 2000The ballot theorem strikes again: packet loss process distribution 1983The throughput time delay function of anM/M/1queue (Corresp.)1982Moment Formulae for a Class of Mixed Multi-Job-Type Queueing Networks

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