Retrial Queueing Model Research Articles

Cost Optimization of MMAP/PH(1), PH(2)/1 Pre-emptive Priority Retrial Queueing model with Standby Server, Orbital Search, Server Breakdowns, Phase Type repairs and Impatient Customers

Cost Optimization of MMAP/PH(1), PH(2)/1 Pre-emptive Priority Retrial Queueing model with Standby Server, Orbital Search, Server Breakdowns, Phase Type repairs and Impatient Customers

Computational Approach for Transient Behaviour of Finite Source Retrial Queueing Model with Multiple Vacations and Negative Arrival

We are analyzing a transient behavior of finite source retrial model with multiple vacations and negative arrival in which the primary arrival rate λ, a Poisson, service time μ, α an exp. distribution. We have assumed that the finite calling population size Fs α obeys an exponential distribution for vacation rate. All transitions are assembled by using an infinitesimal generator matrix (IGM). Cayley Hamilton Method is used to obtain the time dependent and steady state solutions. Computational studies done for analysis of time dependent solutions of mean no. of occupants in the orbit and prob. of server free/busy/vacation for all Fs , λ, μ, α, δ, σ, and t.

An Analysis of a Two-State Markovian Retrial Queueing Model with Priority Customers

Objective: This study considered a system of retrial queues with two types of customers: high-priority and low-priority. This study deals to find the time dependent probabilities of exact number of arrivals and departures from the system when server is free or busy. Numerical solution and graphical representation will also be presented. Method: For this model, we solved difference differential equations recursively and used Laplace transformation to obtain the transient state probabilities of exact number of arrivals and departures from the system when server is free or busy. Findings: Timedependent probabilities of exact number of arrivals (primary arrivals, arrivals in high priority queue, arrivals in low priority queue) in the system and exact number of departures (primary departures, departures from high priority queue, departures from low priority queue) from the system by a given time for when the server is idle and when the server is busy are obtained. Various interesting performance measures along with some special cases are also obtained. Conversion of two state model into single state model was discussed. Numerical illustrations are also presented using MATLAB programming along with the busy period probabilities of the system and server. Novelty: In past research, models considered arrivals and departures from the orbit whereas in present model arrivals and departures from the system are studied along with the concept of retrial and priority customers. Applications: Priority retrial queues are used in many applications like real time systems, operating systems, manufacturing system, simulation and medical service systems. Keywords: Arrivals; Departures; Probability; Priority; Retrial

Analysis of (MAP, PH)/(PH, PH)/1 Retrial Queueing Model with Standby Server, Collision of Orbital Customers, Breakdowns, Two-way communication, Phase Type Repairs, Constant Retrial Rate and Impatient Behaviour of Customers

Analysis of (MAP, PH)/(PH, PH)/1 Retrial Queueing Model with Standby Server, Collision of Orbital Customers, Breakdowns, Two-way communication, Phase Type Repairs, Constant Retrial Rate and Impatient Behaviour of Customers

Analysis of <i>MAP</i><SUB align="right">1<SUP align="right"><i>I</i></SUP>, <i>PH</i><SUB align="right">2<SUP align="right"><i>O</i></SUP>/<i>PH</i><SUB align="right">1<SUP align="right"><i>I</i></SUP>, <i>PH</i><SUB align="right">2<SUP align="right"><i>O</i></SUP>/1 retrial queue with two-way communication, optional service, single vacation, closedown, setup and balking

A single server constant retrial queueing model with close down, vacation, setup, optional service and balking are studied in this article. There are two kinds of arrivals, namely incoming and outgoing calls. If the server is idle, arriving incoming calls will be served instantly. After completion of the service, the server becomes idle. The server goes on vacation, while the system is void. Before taking the vacation, the server will closedown the system and after completion of the vacation, the server will set up the system to give the service. The server will give optional service for incoming calls if the customer needs. The incoming calls follow the Markovian arrival process (MAP) and outgoing calls and service times follow PH-type distribution. We derived the busy period analysis and cost analysis. Also, some important performance measures are obtained which are illustrated graphically/numerically.

Performance Analysis of Retrial Queueing Model with Working Vacation, Interruption, Waiting Server, Breakdown and Repair

In this present paper, an M/M/1 retrial queueing model with a waiting server subject to breakdown and repair under working vacation, vacation interruption is considered. Customers are served at a slow rate during the working vacation period, and the server may undergo breakdowns from a normal busy state. The customer has to wait in orbit for the service until the server gets repaired. Steady-state solutions are obtained using the probability generating function technique. Probabilities of different server states and some other performance measures of the system are developed. The variation in mean orbit size, availability of the server, and server state probabilities are plotted for different values of breakdown parameter and repair rate with the help of MATLAB software. Finally, cost optimization of the system is also discussed, and the optimal value of the slow service rate for the model is obtained.

Performance Analysis in Cellular Networks Considering the QoS by Retrial Queueing Model with the Fractional Guard Channels Policies

In this article, a retrial queueing model will be considered with persevering customers for wireless cellular networks which can be frequently applied in the Fractional Guard Channel (FGC) policies, including Limited FGC (LFGC), Uniform FGC (UFGC), Limited Average FGC (LAFGC) and Quasi Uniform FGC (QUFGC). In this model, the examination on the retrial phenomena permits the analyses of important effectiveness measures pertained to the standard of services undergone by users with the probability that a fresh call first arrives the system and find all busy channels at the time, the probability that a fresh call arrives the system from the orbit and find all busy channels at the time and the probability that a handover call arrives the system and find all busy channels at the time. Comparison between four types of the FGC policy can befound to evaluate the performance of the system.

Analysis of classical retrial queue with differentiated vacation and state dependent arrival rate.

In present paper we have introduced the concept of differentiated vacations in a retrial queueing model with state dependent arrival rates of customers. The arrival rate of customers is different in various states of the server. The vacation types are differentiated by means of their durations as well as the previous state of the server. In type I vacation, server goes just after providing service to at least one customer whereas in type II, it comes after remaining free for some time. In steady state, we have obtained the system size probabilities and other system performance measures. Finally, sensitivity and cost analysis of the proposed model is also performed. The probability generating function technique, parabolic method and MATLAB is used for the purpose.

Retrial queueing model with two heterogeneous server using matrix geometric method

We consider a retrial queuing system with heterogeneous servers. The two servers have service rate µ1 for server 1 and µ2 for server 2 where µ1≠µ2. Server 1 is always obtainable and server 2 is intermittently obtainable. Server 2 goes to execute some important dissimilar jobs when the queue distance is increasing. By introducing the Markov Process {R(t), I(t); t ≥ 0} the stationary analysis has been carried out using Matrix Geometric Technique(MGT). Some numerical outcomes are also obtained.

A Retrial Queueing Model with Scheduling Admission Control in QoS Supporting for FDL-equipped at OBS Core Node

A Retrial Queueing Model with Scheduling Admission Control in QoS Supporting for FDL-equipped at OBS Core Node

A RETRIAL QUEUEING MODEL WITH THRESHOLDS AND PHASE TYPE RETRIAL TIMES

A RETRIAL QUEUEING MODEL WITH THRESHOLDS AND PHASE TYPE RETRIAL TIMES

Sensitivity analysis of the M/M/1 retrial queue with working vacations and vacation interruption

ABSTRACTThis article proposes a methodology, based on the use of a Taylor series expansion, for incorporating epistemic uncertainties in computing performance measures of retrial queueing models. Specifically, we investigate the M/M/1 retrial queue with finite size orbit, working vacation interruption, and classical retrial policy. The sensitivity analysis of the performance measures of the studied model is also provided. This analysis includes the estimation of the expected value and the variance of the performance measures associated with the studied queueing model. The efficiency of the proposed algorithm is assessed on several numerical examples.

A Retrial Queueing model with FDL at OBS core node

Optical Burst Switching networks are considered as an important candidate for the future transport networks. Many analysis models of OBS node with FDLs have been proposed recently. In this paper, we propose a novel retrial queueing model at OBS core node architecture SPL - feed-forward. Blocking probability will be calculated based on Markov multi-dimensional models. Numerical solution values from the proposed analysis method are compared with simulation, as well as between these models.

Light-traffic analysis of random access systems without collisions

We consider a retrial queueing model for random access protocols arising in local area networks such as carrier sense multiple access networks. In our model, one channel is shared among multiple nodes. Each node accesses the channel according to a Poison process and the holding time of the channel is exponentially distributed. Blocked users join the orbit and retry to access again after an exponentially distributed time depending on the number of retrials so far. As the model under study is not amenable for exact analysis, we focus on its performance in the light traffic regime. In particular, we describe a fast algorithm for calculating the terms in the Maclaurin series expansion of various performance measures, the arrival rate being the independent parameter of the expansion. We illustrate our approach by various numerical examples and verify the accuracy of the light traffic approximation by means of simulation.

Retrial Queueing Systems in Series of Space Experiments “Kontur”

This article describes queueing systems model of data transmission system for remote control of robot from board of ISS using public networks. Model has two incoming flows, one service channel, limited buffer size and randomized push-out mechanism. Also model of a retrial queueing system and lost packets with specified probability are able to get back on service. Two parameters: retrial and pushing-out probabilities of randomized mechanism have extremely high influence on model parameters like loss probability and average queue length and allow changing them on tens of percents. Also shown that retrial queueing models are having areas of linear behavior and blocking too, as model without retrial.

Multiserver Queue with Guard Channel for Priority and Retrial Customers

This paper considers a retrial queueing model where a group of guard channels is reserved for priority and retrial customers. Priority and normal customers arrive at the system according to two distinct Poisson processes. Priority customers are accepted if there is an idle channel upon arrival while normal customers are accepted if and only if the number of idle channels is larger than the number of guard channels. Blocked customers (priority or normal) join a virtual orbit and repeat their attempts in a later time. Customers from the orbit (retrial customers) are accepted if there is an idle channel available upon arrival. We formulate the queueing system using a level dependent quasi-birth-and-death (QBD) process. We obtain a Taylor series expansion for the nonzero elements of the rate matrices of the level dependent QBD process. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we develop an efficient numerical algorithm to calculate the joint stationary distribution.

A survey of retrial queueing systems

Retrial queueing systems have been extensively studied because of their applications in telephone systems, call centers, telecommunication networks, computer systems, and in daily life. This survey deals with various retrial queueing models. The main focus of this survey is to show analytic results for queue length distributions, waiting time distributions, and tail asymptotics for the queue length and waiting time distributions. This survey also considers the stability analysis of retrial queueing models.

Performance analysis of a multiprogramming–multiprocessor retrial queueing system with orderly reattempts

This paper deals with retrial queueing models having an unlimited/a finite orbit capacity with control retrial policy of a multiprogramming–multiprocessor computer network system. Under the Markovian assumptions and light-traffic condition, the steady-state probabilities of the number of programs in the system and the mean number of programs in the orbit are studied using matrix geometric/analytic methods. The expressions for the Laplace-Stieglitz transforms of the busy period and the waiting time are obtained. The probability generating function for the number of retrials made by a tagged program is also derived. Some interesting performance measures of the system and the various moments of quantities of interest are discussed. Finally, extensive numerical results are illustrated to reveal the impact of the system parameters on the performance measures.

Retrial queueing models in discrete time: a short survey of some late arrival models

This paper presents an overview of one-server queueing models with retrials in discrete-time. In all these models the number of primary customers arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each customer requires from the server a generally distributed number of slots for his service, and the service times of the different customers are independent. Only models with delayed access are considered, and the so-called late arrival setup is chosen. For all the models the steady-state behavior is studied through the generating function of the number of customers in the orbit. From the generating function several performance measures are deduced, like the average orbit size and the mean busy period.

On a retrial queueing model with single/batch service and search of customers from the orbit

A single server retrial queueing system, where customers arrive according to a batch Poisson process and are served either in single or as a batch, is considered here. An arriving batch, finding the server busy, enters an orbit. Otherwise, one customer, a few customers, or all customers from the arriving batch, depending on if the batch size exceeds a threshold value or not, enter service immediately, while the rest join the orbit. Customers from the orbit try to reach the server subsequently with the inter-retrial times, exponentially distributed. Additionally, at each service completion epoch, one of the two types of search mechanisms say, type I and type II search, to bring the orbital customers to service, is switched on—type I search when the orbit size is less than the threshold value and type II search otherwise. This means that, while the server is idle, a competition takes place among primary customers, customers who come by retrial and by one of the two types of search as the case may be. A type I search selects a single customer whereas a type II search takes a batch of customers from the orbit. In the case of primary customers and those who come by type II search, maximum size of the batch taken into service is restricted to a pre-assigned value. Both single and batch service are assumed to be arbitrarily distributed with different distributions, which are independent of each other. Steady state analysis is performed. Some important system descriptors are computed algorithmically and numerical illustrations are provided.