On product form approximations for communication networks with losses: Error bounds

This paper studies communication networks with packet or message losses due to collisions, transmission errors or finite buffer constraints. Analytic error bounds are derived for simple product form approximations. The approximations are based on ignoring and bounding loss probabilities. The error bounds can be computed easily. Two extreme situations are considered: (1) Networks with infinite capacities but state-dependent loss probabilities; (2) Networks with finite capacities (buffers) and losses due to saturated buffers. The error bounds are of the order β when: (1) the loss probabilities are uniformly bounded by β, or when (2) the steady-state probability of capacity excess is of order β. The results provide formal justification for practical engineering approximations. Extensions to more complex communication networks seem possible.

[1]  Nico M. van Dijk,et al.  A Simple Throughput Bound for Large Closed Queueing Networks with Finite Capacities , 1989, Perform. Evaluation.

[2]  Pramode K. Verma.  Performance estimation of computer communication networks: a structured approach , 1989 .

[3]  Nico M. van Dijk,et al.  Simple Bounds and Monotnicity the Call Congestion of Finite Multiserver Delay Systems , 1988, Probability in the Engineering and Informational Sciences.

[4]  Jan van der Wal,et al.  Simple bounds and monotonicity results for finite multi-server exponential tandem queues , 1989, Queueing Syst. Theory Appl..

[5]  Arie Hordijk,et al.  Networks of queues , 1984 .

[6]  Ivo J. B. F. Adan,et al.  Monotonicity of the Throughput of a Closed Queueing Network in the Number of Jobs , 1989, Oper. Res..

[7]  J. van der Wal,et al.  Monotonicity of the throughput of a closed Erlang queueing network in the number of jobs , 1987 .

[8]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[9]  M. Puterman.  Chapter 8 Markov decision processes , 1990 .

[10]  Nico M. van Dijk,et al.  Simple Bounds for Queueing Systems with Breakdowns , 1988, Perform. Evaluation.

[11]  Nico M. van Dijk.  A formal proof for the insensitivity of simple bounds for finite multi-server non-exponential tandem queues based on monotonicity results , 1987 .

[12]  Henk Tijms,et al.  Stochastic modelling and analysis: a computational approach , 1986 .

[13]  Nico M. Van Dijk,et al.  The Importance of Bias Terms for Error Bounds and Comparison Results , 1989 .

[14]  Nico M. van Dijk.  Approximate uniformization for continuous-time Markov chains with an application to performability analysis , 1988 .

[15]  Ijbf Ivo Adan,et al.  Monotonicity of the throughput in single server production and assembly networks with respect to the buffer sizes , 1987 .