On the GI/M/1/N queue with multiple working vacations—analytic analysis and computation

AbstractWe consider finite buffer single server GI/M/1 queue with exhaustive service discipline and multiple working vacations. Service times during a service period, service times during a vacation period and vacation times are exponentially distributed random variables. System size distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system etc. have been obtained. The model has potential application in the area of communication network, computer systems etc. where a single channel is allotted for more than one source

Queueing models for appointment-driven systems.

Many service systems are appointment-driven. In such systems, customers make an appointment and join an external queue(also referred to as the “waiting list”). At the appointed date, the customer arrives at the service facility, joins an internal queue and receives service during a service session. After service, the customer leaves the system. Important measures of interest include the size of the waiting list, the waiting time at the service facility and server overtime. These performance measures may support strategic decisionmaking concerning server capacity (e.g. how often, when and for how long should a server be online). We develop an ew model to assess these performance measures. The model is a combination of a vacation queueing system and an appointment system.Queueing system; Appointment system; Vacation model; Overtime; Waiting list;

Exact Solutions for M/M/c/Setup Queues

Recently multiserver queues with setup times have been extensively studied because they have applications in power-saving data centers. The most challenging model is the M/M/$c$/Setup queue where a server is turned off when it is idle and is turned on if there are some waiting jobs. Recently, Gandhi et al.~(SIGMETRICS 2013, QUESTA 2014) present the recursive renewal reward approach as a new mathematical tool to analyze the model. In this paper, we derive exact solutions for the same model using two alternative methodologies: generating function approach and matrix analytic method. The former yields several theoretical insights into the systems while the latter provides an exact recursive algorithm to calculate the joint stationary distribution and then some performance measures so as to give new application insights.Comment: Submitted for revie

Performance and economic evaluation of differentiated multiple vacation queueing system with feedback and balked customers

The present paper deals with a single server feedback queueing system under two differentiated multiple vacations and balked customers. It is assumed that the service times of the two vacation types are exponentially distributed with different means. The steady-state probabilities of the model are obtained. Some important performance measures of the system are derived. Then, a cost model is developed. Further, a numerical study is presented

Propagation of epistemic uncertainty in queueing models with unreliable server using chaos expansions

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary distribution of the model, which is a function of uncertain parameters. Polynomial chaos provide an efficient alternative to more traditional Monte Carlo simulations for modelling the propagation of uncertainty arising from those parameters. Furthermore, Polynomial chaos expansion affords a natural framework for computing Sobol' indices. Such indices give reliable information on the relative importance of each uncertain entry parameters. Numerical results show the benefit of using Polynomial Chaos over standard Monte-Carlo simulations, when considering statistical moments and Sobol' indices as output quantities

Two queues with random time-limited polling

In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service times. The server spends an exponentially distributed amount of time in each queue. After the completion of this residing time, the server instantaneously switches to the other queue, i.e., there is no switch-over time. For this polling model we derive the steady-state marginal workload distribution, as well as heavy traffic and heavy tail asymptotic results. Furthermore, we also calculate the joint queue length distribution for the special case of exponentially distributed service times using singular perturbation analysis