A simple derivation of transient queue statistics and applications Academic Article uri icon


  • A simple derivation for the time derivative of a large class of statistics associated with the size of a queue is presented. This method is based on a discrete time approximation in conjunction with conditional expectation and is suitable for any queueing system with multiple interconnected and controlled queues such that the overall dynamics can be modeled as a continuous-time Markov chain. The general procedure is specialized to obtain the Jackson network time-varying kth moment of system size (queue+server) as well as several special cases. Results are also obtained for a network of queues with Erlangian servers. Applications of these results to closure approximations for Jackson networks and to the approximation of statistics of controlled queues are also given. © 1989.

author list (cited authors)

  • Tsai, W. K., & Cantrell, P. E.

citation count

  • 2

publication date

  • November 1989