M/GI/1 MODELS WITH NEGATIVE ARRIVALS TO BE SERVED

On the basic of a type of practical examples we set up a new queueing model with negative customers. By the use of “Supplemental Variables method” and “State transfer analysis”, we get the generating function with negative powers of queue length and the waiting time expressions.

Fluid Model Modulated by an M/M/1 Working Vacation Queue with Negative Customer

This paper investigates a fluid model driven by an M/M/1 queue with working vacations and RCE （Removal of customer in the end） policy of negative customer. In the external environment, the negative customer is not served by the server and only removes the positive customer in the end one-to-one. We establish a fluid flow model based on this stochastic process, and obtain the mean buffer content and the probability of empty buffer for this fluid queue using the LT （Laplace transform） method. Moreover, several special cases of the model here are obtained. Finally, some numerical examples are presented to demonstrate the effects of parameters on the performance indices of the fluid model.

A PERISHABLE INVENTORY SYSTEM WITH SERVICE FACILITIES, MAP ARRIVALS AND PH- SERVICE TIMES

We consider a continuous review perishable （s,S） inventory system with a service facility consisting of a waiting hall of finite capacity and a single server. We assume two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process （MAP）. An ordinary customer joins the queue and a negative customer instead of joining the queue removes one ordinary customer from the queue. The removal rule adopted in this paper is RCE （removal of a customer from the end）. The individual customer＇s unit demand is satisfied after a random time of service which is assumed to have a phase-type distribution. The life time of each item and the lead time of the reorders have been assumed to be independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained for the steady state case. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically.

N-policy for M^(x)/G/1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

Bulk arrival retrial G-queue with impatient customers and multi-servicessubject to server breakdowns has been analyzed. The system allows the arrival oftwo types of customers: positive customers and negative customers in the system.The negative customers make the server fail if they find the server in busy state,whereas positive customers are served if the server is idle otherwise they join thevirtual pool of customers called orbit. The customers from the retrial orbit try theirchance again for the service. The customers have the option of obtaining more than oneservice. Moreover, the customers are impatient and may renege from the system withprobability (1−r ). The server is sent for repair as soon as it breakdowns;after repair,the service process starts again. Also, the server has the provision to initiate the servicewhen there areN customers accumulated in the system. Using supplementary variablestechnique and generating functions, various performance measures like reliabilityindices and long run probabilities have been obtained.