Parallel-Channel, Dual-Resource Constrained Queueing Systems with Heterogeneous Resources

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Abstract
This paper presents an analysis of a class of multi-resource constrained queueing systems. The systems are “job-shop” queueing systems where both machines and laborers are limiting resources. The model consists of M parallel channels, each containing a single machine. Each service channel has its own queue in which an FCFS discipline is enforced. Arrivals to the system are Poisson and are randomly assigned to a specific service channel upon arrival. The labor force consists of N laborers (N < M) who are not equally skilled; thus, the processing time (exponential) is dependent upon the laborer and machine center utilized. Two different means of allocating labor to competing jobs are considered: (1) a first-in-first-out rule, and (2) a maximum laborer efficiency rule. The emphasis of the analysis is on the effects of the pattern of heterogeneity of the labor force and method of labor allocation. GERTS QR, a stochastic network simulation model, is utilized as a vehicle of analysis.

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