Production Systems with Parallel Heterogeneous Servers of Limited Capacity: Accurate Modeling and Performance Analysis

Abstract

Heterogeneous systems of limited capacity have general applications in manufacturing, but also in logistic or service systems due to the differences in server or workstation performance or work assignment; this is in close relationship with system flexibility, where saturation and blocking are ordinary situations of systems with high demand and limited capacity, and thus, accurate loss quantification is essential for performance evaluation. Multi-class systems of limited capacity have been studied much less than parallel homogeneous systems (Erlang models). In this context, accurate models for parallel heterogeneous ordered-entry systems were developed: without any prior queue, i.e., M/Mi/c/c, and with a k-capacity queue, i.e., M/Mi/c/c + k. These new matrix models gave an exact state formulation, and their accuracy was verified using discrete event simulation and comparison with literature results. Also, the effect of the queue capacity was studied in relationship to the pattern of service rates. Next, the heterogeneous recirculating system model was also developed with good approximation results. Finally, the proposed models were applied to evaluate systems with non-exponential service times using a new hybrid methodology by combining the Markovian model and the Monte Carlo method (MCM) for normal or lognormal service times, which also yielded useful good approximations to the simulated system.