Phases Of Heterogeneous Service Research Articles

Reneging in a batch arrival two phases queue with random feedback and Coxian-2 vacation

In this system we consider a batch arrival Poisson input with two phases of heterogeneous service with random feedback in each servivce. The first phase of service is essential for all customers, but with a probability tagged customer chose second phase, feedback to tail of original queue or leave the system. Also, after completion of the second phase, with a probability the customer leaves the system, or feedback to tail of original queue. At each service completion epoch, the server may apt to take a vacation with a probability or continue to be available in the system for the next service. The service times are assumed to be general. The vacation period of the server has two heterogeneous phases with Coxian-2 distribution. The vacation times are assumed to be general. When the server goes for vacation, service become unavailable and customers may decide to renege at each vacation times. We assume reneging follow exponential distribution. All stochastic processes involved in this system (service and vacation times) are independent of each other. We derive the PGF’s of the system and by using them the performance measures are obtained. Some numerical approch are examined the validity of results.

An M/G/1 two phase multi-optional retrial queue with Bernoulli feedback, non-persistent customers and breakdown and repair

This paper has been motivated by the interactive voice response system (IVRS). This system has now become a common phenomenon in our everyday life. In this paper, we consider a Poisson arrival queueing system with a single server and two essential phases of heterogeneous service. The customer who completes the first phase has a choice of k-options to choose for the second phase of service. The customer, who finds the server busy upon arrival, can either join the orbit or he/she can leave the system. After completion of both phases, the customer can decide to try again for service by joining the orbit or he/she can leave the system. The server is subject to sudden breakdowns and repairs. We assume that the breakdowns of the system can occur even when the system is idle. By using the supplementary variables technique, we have obtained the steady state probability generating functions of the orbit size and the system size. We obtain a stochastic decomposition law for the system. We present numerical results ...

A two phase service M/G/1 queue with a finite number of immediate Bernoulli feedbacks

In this paper, we consider an M/G/1 queueing system with two phases of heterogeneous service and a finite number of immediate Bernoulli feedbacks. All arriving customers are provided with the same type of service in the first phase. In the second phase, the customer has to choose from one of the several optional services which are available in the system. After having completed both phases of service, the customer is allowed to make an immediate feedback. The feedback service also consists of two phases. In the feedback, the first phase of service is of the same type as in the previous service. However, in the second phase, the customer may be permitted to choose an optional service different from the one chosen earlier. This feedback scheme is different from the usual Bernoulli feedback scheme. In the earlier papers on the usual Bernoulli feedback, the customer returns to the tail of the queue and waits patiently for his next round of service. In our system, if the customer desires to make a feedback, the customer immediately proceeds for a second round of service after completion of his first round , that is he is his own successor. The customer is allowed to make a finite number of such feedbacks before departing from the system. Our motivation for considering this model comes from our experience in banking transactions through the ATM. We obtain the probability generating function of the system size distribution in the steady state. Some useful performance measures are also obtained. Numerical examples are presented to illustrate the influence of the various parameters involved on the performance of the system.

A single server queueing system with two phases of service subject to server breakdown and Bernoulli vacation

This paper deals with a single server M/G/1 queue with two phases of heterogeneous service and unreliable server. We assume that customers arrive to the system according to a Poisson process with rate λ. After completion of two successive phases of service the server either goes for a vacation with probability p(0⩽p⩽1) or may continue to serve the next unit, if any, with probability q(=1−p). Otherwise it remains in the system until a customer arrives. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. For this model, we first derive the joint distribution of state of the server and queue size, which is one of the chief objectives of the paper. Secondly, we derive the probability generating function of the stationary queue size distribution at a departure epoch. Next, we derive Laplace Stieltjes transform of busy period distribution and waiting time distribution. Finally we obtain some important performance measures and reliability indices of this model.

A batch arrival retrial queue with two phases of service and Bernoulli vacation schedule

We consider an MX/G/1 queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under a linear retrial policy. In addition, each individual customer is subject to a control admission policy upon the arrival. This model generalizes both the classical M/G/1 retrial queue with arrivals in batches and a two phase batch arrival queue with a single vacation under Bernoulli vacation schedule. We will carry out an extensive stationary analysis of the system, including existence of the stationary regime, embedded Markov chain, steady state distribution of the server state and number of customer in the retrial group, stochastic decomposition and calculation of the first moment.

A two-phase queueing system with repeated attempts and Bernoulli vacation schedule

This paper deals with the steady-state behaviour of an M/G/1 queue with repeated attempts in which the server provides two phases of heterogeneous service under Bernoulli vacation schedule. We carry out an extensive analysis of the system, including existence of stationary regime, embedded Markov chain, steady-state distribution of the server state and the number of customer in the orbit and some system performance measures. This model generalises both the classical M/G/1 retrial queue and the M/G/1 queue with two phases of service and Bernoulli vacation model.

On the Single Server Batch Arrival Retrial Queue with General Vacation Time under Bernoulli Schedule and Two phases of Heterogeneous Service

We consider a single server retrial queue with batch arrivals, two phases of heterogeneous service and a general vacation time under Bernoulli schedule. We carry out steady state system size distribution of number of customers in retrial group, expected number of customers in retrial group and expected waiting time of the customers in the orbit. We discuss its application of the proposed model to the analysis of a communication protocol.

Steady state analysis of an M/G/1 queue with linear retrial policy and two phase service under Bernoulli vacation schedule

We consider a single server queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under the so called linear retrial policy. This model extends both the classical M / G / 1 retrial queue with linear retrial policy as well as the M / G / 1 queue with two phases of service and Bernoulli vacation model. We carry out an extensive analysis of the model.

A two phase batch arrival retrial queueing system with Bernoulli vacation schedule

We consider an M x / G/1 queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under classical retrial policy. In addition, each individual customer is subject to a control admission policy upon the arrival. This model generalized both the classical M/ G/1 retrial policy with arrivals in batches and a two phase batch arrival queue with single vacation under Bernoulli vacation schedule. We will carry out an extensive stationary analysis of the system, including existence of the stationary regime, embedded Markov chain, steady state distribution of the server state and number of customer in the retrial group, stochastic decomposition and calculation of the first moments.

Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.

A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p ( 0 ≤ p ≤ 1 ) or may continue to serve the next unit, if any, with probability q ( = 1 − p ) . Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues.

A two phase batch arrival queueing system with a vacation time under Bernoulli schedule

We consider a batch arrival queueing system, where the server provides two phases of heterogeneous service one after the other to the arriving batches under Bernoulli schedule vacation. After completion of both phases of service the server either goes for a vacation with probability r(0⩽ r⩽1) or may continue to serve the next unit, if any, with probability (1− r). Otherwise, it remains in the system until a new batch of customers arrives. We derive the queue size distribution at a random epoch as well as a departure epoch under the steady state conditions. Further, we derive some important performance measures of this system. This extends the model studied by Madan [Egyptian Statist. J. 44 (2000) 39; Int. J. Syst. Sci. 32 (2001) 837].

A batch arrival queue with an additional service channel under N-policy

This paper deals with an M x / G/1 queueing system with two phases of heterogeneous service under N-policy, where the server remains idle till the queue size becomes N(⩾1). As soon as the queue size becomes N, the server immediately starts first `essential service' for all the units. After completion of the essential service of a unit, it may leave the system with probability (1− θ) or may immediately go for a second phase of service in an additional service channel with probability θ (0⩽ θ⩽1). For this model, we derive the queue size distribution at a random epoch as well as at a departure epoch. Further, we derive some important performance measures of this model. This is a generalization of recent papers considered by Medhi [Queueing Systems 42 (2002) 239] and Lee et al. [Queueing Systems 15 (1994) 387].