A queueing model of a production system with two machines,one operator and priorities

This paper studies a priority queueing model of a production system in which one operator serves two types of units with overlapping service times. The two types of units arrive in independent Poisson processes. There are two machines in the system. Units of type 1 receive two consecutive types of services at machine #1: the handwork performed by the operator and the automatic machining without the operator. Units of type 2 receive only the handwork performed by the operator at machine #2. The operator attends the two machines according to a strict-priority discipline which always gives units of type 2 higher priority than units of type 1. At each machine the handwork times have a general distribution, and at machine #1 the machining times have an exponential distribution. The Laplace-Stieltjes transform of the queue-size distributions and the waiting time distributions for a stationary process are obtained.     

Saturation in Linear Optimization

In a solvable linear optimization problem, a constraint is saturated if it is binding at a certain optimal solution and it is weakly saturated if it is binding at a proper subset of the optimal set. Nonsaturation and weak saturation can be seen as redundancy phenomena in the sense that the elimination of a finite number of these constraints preserves the value of the given problem. We consider also the effect of sufficiently small perturbations of the cost coefficients in the classification of a given constraint as either saturated or nonsaturated.