Waiting times in a two-queue model with exhaustive and Bernoulli service

This paper deals with waiting times in a two-queue polling system in which one queue is served according to the Bernoulli service discipline and the other one attains exhaustive service. Exact results are derived for the LST's of the waiting time distributions via an iteration scheme. Based on those results the mean waiting times are expressed in the system parameters.     

A two-queue,one-server model with priority for the longer queue

The queueing model studied consists of one server and two queues. Each queue has its own Poisson arrival stream and service time distribution. After a service completion, the server proceeds with a customer from the longer queue, if the queues are unequal; if the queues are equal, the server chooses with some probability a customer from one of the queues. The model is of practical interest in performance analysis, but also of theoretical interest because the functional equation to be solved has not yet been studied in the queueing literature. A basic analysis of this functional equation is presented. Some numerical results are given to assess the influence of the present service discipline. Some new properties of L.S. transforms of service time distributions are discussed in the appendix.Dr. T. Katayama has formulated the present problem and brought it to the author's attention during his visit in October/November 1984 to the NTT-Electr. Comm. Lab.'s Musashino, Tokyo 180.     

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 batch arrival retrial queue with two phases of service and 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 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 batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delaying repair

This paper deals with the steady state behaviour of an M^x/G/1 queue with general retrial time and Bernoulli vacation schedule for an unreliable server, which consists of a breakdown period and delay period. Here we assume that customers arrive according to compound Poisson processes. While the server is working with primary customers, it may breakdown at any instant and server will be down for short interval of time. Further concept of the delay time is also introduced. The primary customer finding the server busy, down or vacation are queued in the orbit in accordance with FCFS (first come first served) retrial policy. After the completion of a service, the server either goes for a vacation of random length with probability p or may continue to serve for the next customer, if any with probability (1 − p). We carry out an extensive analysis of this model. Finally, we obtain some important performance measures and reliability indices of this model.     

Start‐up demonstration tests: models,methods and applications,with some unifications

Start‐up demonstration tests were first discussed in the quality/reliability literature about three decades ago. Since then, many variations of these tests have been introduced, and the corresponding distributional characteristics and inferential methods have also been studied. All these developments, based on independent and identically distributed binary trials, have been further generalized to some other forms of trials such as Markov‐dependent trials, exchangeable trials and multistate trials. In this paper, we provide a comprehensive review of all these results and highlight some unifications of the results. We also describe a general estimation method and then present several numerical examples to illustrate some of the models and methods described here. Finally, a number of open issues in this area of research are pointed out. Copyright © 2014 John Wiley & Sons, Ltd.