In this paper we survey work related to queues with interruptions that occur due to many reasons such as server breakdowns, servers taking emergency breaks, and customers having incomplete information or getting distracted We look at both continuous and discrete time queueing models with interruptions in this survey

Queues with interruptions: a survey

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

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

Reliability analysis of a k-out-of-n:G repairable system with single vacation

This paper concerns the reliability issues as well as queueing analysis M/G/1 retrial queues with general retrial times and server subject to breakdowns and repairs. We assume that the server is unreliable and customers who find the server busy or down are queued in the retrial orbit in accordance with a firs-come-first-served discipline. Only the customer at the head of the orbit queue is allowed for access to the server. The necessary and sufficient condition for the system to be stable is given. Using a supplementary variable method, we obtain the Laplace-Stieltjes transform of the reliability function of the server and a steady state solution for both queueing and reliability measures of interest. Some main reliability indexes, such as the availability, failure frequency, and the reliability function of the server, are obtained. * Supported by Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, National Natural Science Foundation of China (Gran...

Reliability analysis M/G/1 queues with general retrial times and server breakdowns

An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.

An M/G/1 retrial queue with second multi-optional service, feedback and unreliable server

In this paper we consider the system of M/M/N queue with server breakdowns plus balking and reneging,the rates of server breakdown are different from busy time and idle time,and there is one repairman in the system.We derive the steady state distribution of the number of effective servers,the moment generating function of the steady state queue length and the system performance measures.

M/M/N Queue System with Balking Reneging and Server Breakdowns

We consider an M/G/1 retrial queue with two-phase service and unreliable server.All customers demand the first essential service,whereas only some of them demand the second "multi-optional" service.It is assumed that the service time and repair time of two phases are all generally distributed.By applying the supplementary variables method,we obtain the steady-state solutions for both queuing measures and reliability quantities of the server.

An M/G/1 Retrial Queue with Second Multi-Optional Service and Server Breakdowns

We consider a discrete-time Geo/G/1 retrial queue with starting failure where all the arriving customers finish their service while only some of them returns to the orbit for another service.We study the Markov chain underlying the considered queueing system and its ergodicity condition.We present some performance measures of the system in steady-state.Then,we give two stochastic decomposition laws.Finally,some numerical examples show the influence of the parameters on several performance characteristics.

Wang Jinting

Papers

Reliability analysis M/G/1 queues with general retrial times and server breakdowns

An M/G/1 retrial queue with second multi-optional service, feedback and unreliable server

M/M/N Queue System with Balking Reneging and Server Breakdowns

An M/G/1 Retrial Queue with Second Multi-Optional Service and Server Breakdowns

A Discrete-Time Retrial Queue with Starting Failure and Feedback