فهرس المقالات Supplementary variable

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  1 - Analysis of unreliable bulk queue with statedependent arrivals
  Charan Jeet Singh Madhu Jain Binay Kumar
  In this paper, we investigate a single-server Poisson input queueing model, wherein arrivals of units are in bulk. The arrival rate of the units is state dependent, and service time is arbitrary distributed. It is also assumed that the system is subject to breakdown, أکثر

  In this paper, we investigate a single-server Poisson input queueing model, wherein arrivals of units are in bulk. The arrival rate of the units is state dependent, and service time is arbitrary distributed. It is also assumed that the system is subject to breakdown, and the failed server immediately joins the repair facility which takes constant duration to repair the server. By using supplementary variable technique, we obtain the probability generating function of the number of units in the system which is further used to establish some performance indices such as the mean number of units in the system, mean waiting time, etc. Special cases are also discussed. In order to obtain approximate values of system state probabilities, the principle of maximum entropy is employed. Numerical results are also presented to validate the analytical formulae. تفاصيل المقالة
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  2 - Unreliable bulk retrial queues with delayed repairs and modified vacation policy
  Madhu Jain Amita Bhagat
  The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy. The incoming customers join the virtual pool of customers called orbit if they find the server being busy, on vacation or in broken down stat أکثر

  The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy. The incoming customers join the virtual pool of customers called orbit if they find the server being busy, on vacation or in broken down state otherwise the service of the customer at the head of the batch is started by the server. The service is provided inkessential phases to all the customers by the single server which may breakdown while rendering service to the customers. The broken down server is sent to a repair facility wherein the repair is performed indcompulsory phases. As soon as the orbit becomes empty, the server goes for vacation and takes at mostJvacations until at least one customer is noticed. The incoming customers are impatient and may renege on seeing a long queue of the customers for the service. The probability generating functions and queue length for the number of customers in the orbit and queue have been obtained using supplementary variable technique. Various system characteristics viz. average number of customers in the queue and the orbit, long run probabilities of the system states, etc. are obtained. Furthermore, numerical simulation has been carried out to study the sensitivity of various parameters on the system performance measures by taking an illustration. تفاصيل المقالة
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  3 - Analysis of M/G/ 1 queueing model with state dependent arrival and vacation
  Charan Jeet Singh Madhu Jain Binay Kumar
  This investigation deals with single server queueing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a vacation of a f أکثر

  This investigation deals with single server queueing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a vacation of a fixed duration or may continue to be available in the system for next service. Using the probability argument, we construct the set of steady state equations by introducing the supplementary variable corresponding to elapsed service time. Then, we obtain the probability generating function of the units present in the system. Various performance indices, such as expected number of units in the queue and in the system, average waiting time, etc., are obtained explicitly. Some special cases are also deduced by setting the appropriate parameter values. The numerical illustrations are provided to carry out the sensitivity analysis in order to explore the effect of different parameters on the system performance measures. تفاصيل المقالة
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  4 - DISCRETE-TIME GI/D-MSP/1/K QUEUE WITH N THRESHOLD POLICY
  Veena Goswami P. Vijaya Laxmi
  This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discreteMarkovian service process. The server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting cu أکثر

  This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discreteMarkovian service process. The server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting customers in the queue is N. We obtain the system-length distributionsat pre-arrival and arbitrary epochs using the supplementary variable and the imbedded Markov chain techniques.Various performance measures such as the loss probability, mean queue length and mean waiting time in the queue along with some numerical results have been presented. The proposed model has potential applications in the areas of computer andtelecommunication systems. تفاصيل المقالة
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  5 - FINITE POPULATION SINGLE SERVER BATCH SERVICE QUEUE WITH COMPULSORY SERVER VACATION
  Rathinasabapathy Kalyanaraman R. Mahalakshmi
  A single server finite population queueing model with compulsory server vacation and with fixed batch service has been considered. For this model the system steady state probabilities are obtained. Some performance measures are calculated and numerical examples are also أکثر

  A single server finite population queueing model with compulsory server vacation and with fixed batch service has been considered. For this model the system steady state probabilities are obtained. Some performance measures are calculated and numerical examples are also given. تفاصيل المقالة
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  6 - AN M/G/1 QUEUE WITH REGULAR AND OPTIONAL PHASE VACATION AND WITH STATE DEPENDENT ARRIVAL RATE
  Rathinasabapathy Kalyanaraman Shanthi R
  We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there areno customers in the system, the server takes vacation consisting of K -phases, each phaseis generally أکثر

  We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there areno customers in the system, the server takes vacation consisting of K -phases, each phaseis generally distributed. Here the first phase is compulsory where as the other phases areoptional. For this model the supplementary variable technique has been applied to obtainthe probability generating functions of number of customers in the queue at the different server states. Some particular models are obtained and a numerical study is also carriedout. تفاصيل المقالة
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  7 - A SINGLE SERVER BERNOULLI VACATION QUEUE WITH TWO TYPE OF SERVICES AND WITH RESTRICTED ADMISSIBILITY
  R. Kalyanaraman V. Suvitha
  A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue a أکثر

  A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. Some performance measures are calculated. Some particular cases are obtained and numerical examples are also presented. تفاصيل المقالة
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  8 - ANALYSIS OF RENEWAL INPUT STATE DEPENDENT VACATION QUEUE WITH $N$-POLICY
  Vijaya Laxmi Pikkala Suchitra Vepada
  This paper analyzes renewal input state dependent queuewith $N$- policy wherein the server takes exactly one vacation.Using the supplementary variable technique and recursive method,we derive the steady state system length distributions at various epochs.Various perform أکثر

  This paper analyzes renewal input state dependent queuewith $N$- policy wherein the server takes exactly one vacation.Using the supplementary variable technique and recursive method,we derive the steady state system length distributions at various epochs.Various performance measures has been presented. Finally, some numericalcomputations in the form of graphs are presented to show the parametereffect on various performance measures. تفاصيل المقالة