Throughput monotonicity in communication networks with blocking: properties and counterexamples

The authors study the effect of increasing buffer capacities on the performance of queuing networks that use probabilistic or state-dependent routing. The approach is to establish strong stochastic ordering relations on several performance measures using sample path arguments. In particular, it is proved that the throughput is monotonically increasing with respect to an overall capacity vector in networks with exponential service times, or deterministic service times and synchronous transmission. However, in networks with deterministic service times and asynchronous transmission this property may not hold, as seen through a counterexample. A simple retransmission algorithm is proposed to overcome this problem. Finally, the monotonicity property is also shown to hold in tandem networks with exponential servers where blocked customers are retransmitted rather than rejected