Two-Moment Phase-Type Fitting for ASIP Tandem Systems

The asymmetric simple inclusion process (ASIP) is an n-site tandem stochastic network used to model clustered particle flow. Particles at each site form a cluster that moves to the next site when its gate opens. For the general ASIP, no closed-form expression exists for the load in terms of the first two moments of the interarrival and inter-gate opening time distributions. We approximate the steady-state load by fitting a phase-type ASIP using a two-moment approach. We obtain a recursive expression for the site-occupancy PGF and a closedform PGF for the steady-state load, enabling a closed-form approximation of its expectation. Our results show that interarrival and inter-gate opening distributions have opposite effects on the load. Further, contrary to typical performance evaluation of queuing systems, our results indicate that systems with more unreliable servers (increased inter-gate opening time variance) exhibit superior expected performance, assuming that the servers’ expected performance is equivalent.