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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A queue with skill based service under FCFS-ALIS : steady state, overloaded system, and behavior under abandonments

We consider a queueing system with servers S = {m_1, …, m_J}, and with customer types C = {a, b, …}. A bipartite graph G describes which pairs of server - customer type are compatible. We consider FCFS-ALIS policy: A server always picks the first, longest waiting compatible customer, a customer is always assigned to the longest idle compatible server. We assume Poisson arrivals and exponential service times. We derive an explicit product-form expression for the steady state distribution of this system when service capacity is sufficient. We analyze the system under overload, when partial steady state exists. Finally we describe the behavior of the system with generally distributed abandonments, under many arrivals - fast service scaling