M/G/1 Queue with Negative Arrival and Breakdown
نویسنده
چکیده
The author considers a batch arrival queueing system in which two types of customers (namely positive and negative) arrive. The arrival of a negative customer to a queueing system removes one positive customer who is in service if any. A cycle starts whenever the system empties and the server is turned off and stays idle in the system. The idle period ends as soon as a batch of positive customers arrives for services. The positive customer who is in the head of queue will join the service immediately. The arrival of negative customers causes the server to breakdown. Whenever the server fails, it is sent to repair facility. The arriving negative customers during the idle period are assumed to be lost. Immediately after the server is fixed the customer waiting in the head of the queue is taken up for service. In the present paper, the author analyzes steady state behavior of the system size distribution of M/G/1 queue with negative customers. The probability generating function (PGF) of the stationary queue length are presented and performance measures are obtained. Numerical examples to illustrate the effect of the parameters are also provided.
منابع مشابه
Single Server Bulk Queue with Service Interruption, Two Phase Repairs and State Dependent Rates
This paper reports a study on a single server queue with bulk arrival and bulk service patterns wherein the incoming traffic depends on the state of the server which may be in operating or breakdown state. The repair of the breakdown server is performed in two phases. The operating duration of server, repair duration of both phases of repairing as well as job's inter-arrival times and service t...
متن کاملAN M/G/1 QUEUE WITH REGULAR AND OPTIONAL PHASE VACATION AND WITH STATE DEPENDENT ARRIVAL RATE
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 are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...
متن کاملUnreliable Server Mx/G/1 Queue with Loss-delay, Balking and Second Optional Service
This investigation deals with MX/G/1 queueing model with setup, bulk- arrival, loss-delay and balking. The provision of second optional service apart from essential service by an unreliable server is taken into consideration. We assume that the delay customers join the queue when server is busy whereas loss customers depart from the system. After receiving the essential service, the customers m...
متن کاملMaximum Entropy Analysis for G/G/1 Queuing System (TECHNICAL NOTE)
This paper provides steady state queue-size distribution for a G/G/1 queue by using principle of maximum entropy. For this purpose we have used average queue length and normalizing condition as constraints to derive queue-size distribution. Our results give good approximation as demonstrated by taking a numerical illustration. In particular case when square coefficient of variation of inter-arr...
متن کاملThe Workload in the M / G / 1 Queue with Work
We consider an M/G/1 queue with the special feature of additional negative customers, who arrive according to a Poisson process. Negative customers require no service, but at their arrival a stochastic amount of work is instantaneously removed from the system. We show that the workload distribution in this M/G/1 queue with negative customers equals the waiting time distribution in a GI/G/1 queu...
متن کامل