A product form solution to a system with multi-type jobs and multi-type servers

Abstract

We consider a memoryless single station service system with servers S = {m 1 , . . . , m K }, and with job types C = {a, b, . . .}. Service is skill-based, so that server m i can serve a subset of job types C(m i ). Waiting jobs are served on a first-come-firstserved basis, while arriving jobs that find several idle servers are assigned to a feasible server randomly. We show that there exist assignment probabilities under which the system has a product-form stationary distribution, and obtain explicit expressions for it. We also derive waiting time distributions in steady state.

A skill based parallel service system under FCFS-ALIS — steady state, overloads, and abandonments

“…We conjecture that specifying the customer types in service will destroy the possibility of a product form solution. This was also indicated in Proposition 8, Section 2, of [35], which illustrates the subtlety of the definition of the system state, being crucial to the existence of product forms.…”

Exact FCFS Matching Rates for Two Infinite Multitype Sequences

“…The formula (7) is then derived from the stationary distribution. The Markov chain which we use to describe the matching process uses the same idea which was used by Visschers et al [9,10] to describe a queueing system with multi-type customers and multi-type servers.…”

“…In Section 3 we obtain the formula (7) for the matching rates. In Sections 5 and 6 we explore the relationship between our model and the manufacturing type queueing system of Visschers et al [9,10] and the call center skilled based routing type model of Whitt and Talreja [8].…”

Queues with skill based parallel servers and a FCFS infinite matching model

“…A more general FCFS infinite matching model was described in [5]. The infinite matching model was found to be closely related to several queueing models with skill based parallel service [11,2]. Here we present some novel results.…”