Queueing Systems

, Volume 28, Issue 1, pp 55–77

Bounding blocking probabilities and throughput in queueing networks with buffer capacity constraints


  • Sunil Kumar
    • Graduate School of BusinessStanford University
  • R. Srikant
    • Department of General Engineering, and the Coordinated Science LaboratoryUniversity of Illinois
  • P.R. Kumar
    • Department of Electrical Engineering, and the Coordinated Science LaboratoryUniversity of Illinois

DOI: 10.1023/A:1019142905175

Cite this article as:
Kumar, S., Srikant, R. & Kumar, P. Queueing Systems (1998) 28: 55. doi:10.1023/A:1019142905175


We propose a new technique for upper and lower bounding of the throughput and blocking probabilities in queueing networks with buffer capacity constraints, i.e., some buffers in the network have finite capacity. By studying the evolution of multinomials of the state of the system in its assumed steady state, we obtain constraints on the possible behavior of the system. Using these constraints, we obtain linear programs whose values upper and lower bound the performance measures of interest, namely throughputs or blocking probabilities. The main advantages of this new technique are that the computational complexity does not increase with the size of the finite buffers and that the technique is applicable to systems in which some buffers have infinite capacity. The technique is demonstrated on examples taken from both manufacturing systems and communication networks. As a special case, for the M/M/s/s queue, we establish the asymptotic exactness of the bounds, i.e., that the bounds on the blocking probability asymptotically approach the exact value as the degree of the multinomials considered is increased to infinity.

queueing networks communication networks performance evaluation finite buffers blocking

Copyright information

© Kluwer Academic Publishers 1998