A discrete-time retrial queue with negative customers and unreliable server

Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers

Bibliography on G-networks, negative customers and applications

This paper aims at presenting an analytic approach for investigating a single-server retrial queue with finite population of customers where the server is subject to interruptions. A free source may generate a primary call to request service. If the server is free upon arrival, the call starts to be served and the service times are independent, generally distributed random variables. During the service time the source cannot generate a new primary call. After service the source moves into the free state and can generate a new primary call. There is no waiting space in front of the server, and a call who finds the server unavailable upon arrival joins an orbit of unsatisfied customers. The server is subject to interruptions during the service processes. When the server is interrupted, the call being served just before server interruption goes to the retrial orbit and will retry its luck after a random amount of time until it finds the server available. The recovery times of the interrupted server are assumed to be generally distributed. Our analysis extends previous work on this topic and includes the analysis of the arriving customer’s distribution, the busy period, and the waiting time process.

Performance analysis of the retrial queues with finite number of sources and service interruptions

This paper is concerned with the queueing analysis as well as
reliability evaluation of an $M/G/1//K$ retrial queue with a finite
number of sources in which the server is subject to breakdowns and
repairs. The server has a exponentially distributed life time and a
generally distributed repair time. Our analysis extends previous
work on this topic and includes the analysis of the arriving
customer's distribution, the busy period, the waiting time process
and main reliability characteristics. This queueing system and its
variants could be used to model magnetic disk memory systems,
star-like local area networks and other communication systems with
detected or undetected breakdowns.

Analysis of the finite source retrial queues withserver breakdowns and repairs

Transient analysis of an M/G/1 retrial queue subject to disasters and server failures

An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first “essential” service, whereas only some of them demand the second “optional” service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest.

A single server retrial queue with general retrial times and two-phase service

A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a servicephase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.

Analysis of the M[X]/G/1 queues with second multi-optional service and unreliable server

A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first "essential" service, whereas only some of them demand the second "multi-optional" service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a service- phase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.

Jiang-hua Li

Papers

Transient analysis of an M/G/1 retrial queue subject to disasters and server failures

A single server retrial queue with general retrial times and two-phase service

Analysis of the M[X]/G/1 queues with second multi-optional service and unreliable server

M (X) /G/1 Queues with Second Multi-optional Service and Unreliable Server