A Loss System With Skill-Based Servers Under Assign to Longest Idle Server Policy

Abstract

We consider a memoryless loss system with servers ${\cal S}$ = {1, …, J}, and with customer types ${\cal C}$ = {1, …, I}. Servers are multi-type: server j works at rate μj, and can serve a subset of customer types C(j). An arriving customer will go to the longest idling server which can serve him, or be lost. We obtain a simple explicit steady-state distribution for this system, and calculate various performance measures of this system in steady state. We provide some illustrative examples. We compare this system with a similar system discussed recently by Adan, Hurkens, and Weiss [1]. We also show that this system is insensitive, the results hold also for general service time distributions.

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

“…The proof of Theorem 2.2 is given in Appendix A.2, and it is based on the proof of a similar result for a skill based service Erlang loss system [3,5].…”

On the Adan–weiss Loss Model Having Skill-Based Servers and Longest Idle Assignment Rule

“…Our approach will be to conjecture the reverse chain, and then show the conjecture is correct by finding, up to a multiplicative constant, the limiting probabilities of the ordered list of idle servers. We also show that given the set of busy servers, the remaining service times are independent with their respective equilibrium distributions (This result is only implicitly noted in Adan and Weiss [2].) In practice, when n is large finding the limiting probabilities or any other quantity of interest becomes computationally intractable.…”

“…In [2], Adan and Weiss introduced a queueing loss model with n servers having arbitrary service distributions, G i , i = 1, . .…”

Dynamic Load Balancing with Tokens

“…Some recent works have tackled this problem from the point of view of queueing theory [1,15,9,4]. Their common feature is the adoption of a bipartite graph that translates practical constraints such as data locality into compatibility relations between jobs and servers.…”

“…However, these pool models do not consider simultaneously the impact of complex load balancing and resource allocation policies. The model of [1] lays emphasis on dynamic load balancing, assuming neither server multitasking nor job parallelism. The bipartite graph describes the initial compatibilities of incoming jobs, each of them being eventually assigned to a µ 1…”