Dependence in packet queues

The burstiness of the total arrival process has been previously characterized in packet network performance models by the dependence among successive interarrival times. It is shown that associated dependence among successive service times and between service times and interarrival times also can be important for packet queues involving variable packet lengths. These dependence effects are demonstrated analytically by considering a multiclass single-server queue with batch-Poisson arrival processes. For this model and more realistic models of packet queues, insight is gained from heavy-traffic limit theorems. This study indicates that all three kinds of dependence should be considered in the analysis and measurement of packet queues involving variables packet lengths. Specific measurements are proposed for real systems and simulations. This study also indicates how to predict expected packet delays under heavy loads. Finally, this study is important for understanding the limitations of procedures such as the queuing network analyzer (QNA) for approximately describing the performance of queuing networks using the techniques of aggregation and decomposition. >