MAP-Based Decomposition of Tandem Networks of ./PH/1(/K) Queues with MAP Input.
Armin Heindl, Miklós Telek · 2001
For non-trivial (open) queueing networks and also for tandem queueing networks, decomposition often represents the only feasible solution method besides simulation. The network is partitioned into individual nodes which are analyzed in isolation with respect to approximate internal trac representations. The quality of the quickly obtainable results very much depends on the descriptors for the traffic processes within the network. In this paper, the decomposition of tandem networks is based on Markovian arrival processes (MAPs), which allow to capture the correlations in the traffic processes. The correlation structure of network traffic is known to have a considerable impact on performance measures. Moreover, MAP inputs considerably increase the range of applications of the queueing networks with phase type service times and customer losses. Numerical experiments on tandem networks demonstrate the accuracy of the newly proposed approach, which may be extended to general queueing networks with Markovian routing.