Mathematics Colloquium

Add to Calendar 01/24/2017 15:35:0001/24/2017 16:30:0015Mathematics ColloquiumSpeaker: James D. Cordeiro, MediaDyne Systems Engineering Title: A Markov-Modulated M/M/1 Retrial Queue with Unreliable Server Abstract: In this talk, I will examine a single-server retrial queue whose parameters are modulated by an exogenous stochastic process (i.e., a random environment). In a retrial service system, arriving customers who find the server busy or failed join an auxiliary retrial queue, or orbit, from which they persistently attempt to gain access to the server at random intervals. Customers also join the orbit if their service session is interrupted by a server failure. Retrial systems find wide applicability in the performance evaluation of computer and communication systems that are subject to a variety of operating conditions (e.g., varying service demand levels, harsh operating environments, etc.). We analyze an M/M/1 version of such a system whose arrival, service, retrial, failure and recovery rates are modulated by an exogenous process. We show that the joint process of orbit size, environment state, and server status can be viewed as a level-dependent quasi-birth-and-death (LDQBD) process and employ matrix-analytic methods to approximate its limiting distribution. Additionally, using a classical theorem by Foster (1953), we establish ergodicity conditions for generalized LDQBD processes that facilitate an explicit stability result for the retrial system. Refreshments are available at 3:00 PM in SC 313F. The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. Science Center Room 323Paul Eloepeloe1@udayton.eduNo01/24/2017

Tuesday, January 24

Time: 3:35 p.m. — 4:30 p.m.

Location: Science Center Room 323

Tags:  Arts and Sciences, Colloquia, Mathematics, Sciences

Cost:  Free

Speaker: James D. Cordeiro, MediaDyne Systems Engineering

Title: A Markov-Modulated M/M/1 Retrial Queue with Unreliable Server

Abstract: In this talk, I will examine a single-server retrial queue whose parameters are modulated by an exogenous stochastic process (i.e., a random environment). In a retrial service system, arriving customers who find the server busy or failed join an auxiliary retrial queue, or orbit, from which they persistently attempt to gain access to the server at random intervals. Customers also join the orbit if their service session is interrupted by a server failure. Retrial systems find wide applicability in the performance evaluation of computer and communication systems that are subject to a variety of operating conditions (e.g., varying service demand levels, harsh operating environments, etc.). We analyze an M/M/1 version of such a system whose arrival, service, retrial, failure and recovery rates are modulated by an exogenous process. We show that the joint process of orbit size, environment state, and server status can be viewed as a level-dependent quasi-birth-and-death (LDQBD) process and employ matrix-analytic methods to approximate its limiting distribution. Additionally, using a classical theorem by Foster (1953), we establish ergodicity conditions for generalized LDQBD processes that facilitate an explicit stability result for the retrial system.

Refreshments are available at 3:00 PM in SC 313F.

The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. 

Contact Information:

Name:  Paul Eloe
Email:  peloe1@udayton.edu