An approximate analysis of a bernoulli alternating service model

We consider a discrete-time queueing system with one server and two types of customers, say type-1 and type-2 customers. The server serves customers of either type alternately according to a Bernoulli pro- cess. The service times of the customers are deterministically equal to 1 time slot. For this queueing system, we derive a functional equation for the joint probability generating function of the number of type-1 and type-2 customers. The functional equation contains two unknown partial generating functions which complicates the analysis. We investigate the dominant singularity of these two unknown functions and propose an approximation for the coefficients of the Maclaurin series expansion of these functions. This approximation provides a fast method to compute approximations of various performance measures of interest

Exact and Approximate Analysis of Multi-Echelon, Multi-Indenture Spare Parts Systems with Commonality

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Combining make to order and make to stock

In inventory control and production planning one is tempted to use one of two strategies: produce all demand to stock or produce all demand to order. The disadvantages are well-known. In the make everything to order case (MTO) the response times may become quite long if the load is high, in the make everything to stock case (MTS) one gets an enormous inventory if the number of different products is large. In this paper we study two simple models which combine MTO and MTS, and investigate the effect of combining MTO and MTS on the production lead times

Analysing shortest expected delay routing for Erlang servers

The queueing problem with a Poisson arrival stream and two identical Erlang servers is analysed for the queueing discipline based on shortest expected delay. This queueing problem may be represented as a random walk on the integer grid in the first quadrant of the plane. In the paper it is shown that the equilibrium distribution of this random walk can be written as a countable linear combination of product forms. This linear combination is constructed in a compensation procedure. In this case the compensation procedure is essentially more complicated than in other cases where the same idea was exploited. The reason for the complications is that in this case the boundary consists of several layers which in turn is caused by the fact that transitions starting in inner states are not restricted to end in neighbouring states. Good starting solutions for the compensation procedure are found by solving the shortest expected delay problem with the same service distributions but with instantaneous jockeying. It is also shown that the results can be used for an efficient computation of relevant performance criteria