Analytical Study of Two Serial Channels with Priority and Reneging

Most of the studies of queuing theory, which are useful in our daily life has been investigated by many researchers. The present research is the study of pre-emptive priority queuing system consisting two serial channels in stochastic environment. The impatient behavior of customer’s will be discussed with exponential service distribution and Poisson arrivals. Higher priority customers have pre-emptive priority over the low priority customers. The G.F. technique is used to derive the performance measures of high & low priority queues and assuming FCFS discipline in busy schedule of higher priority class. Also evaluate queue behavior graphically and discussed a special case at the end which shows utilization of channels

Estimating customer impatience in a service system with unobserved balking

This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. The main objective is to estimate the customers' patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual queue-length process only. The main complication, and distinguishing feature of our setup, lies in the fact that customers who decide not to join are not observed, but, remarkably, we manage to devise a procedure to estimate the load they would generate. We express our system in terms of a multi-server queue with a Poisson stream of customers, which allows us to evaluate the corresponding likelihood function. Estimating the unknown parameters relying on a maximum likelihood procedure, we prove strong consistency and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. The performance of our approach is further assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized-hyperexponential distributions our method provides a robust estimation framework for any continuous patience-level distribution

Stationary Analysis of a Multiserver queue with multiple working vacation and impatient customers

We consider an M/M/c queue with multiple working vacation and impatient customers. The server serves the customers at a lower rate rather than completely halts the service during this working vacation period. The impatience of the customer’s arises when they arrive during the working vacation period, where the service rate of the customer’s is lower than the normal busy period. The queue is analyzed for multiple working vacation policies. The policy of a MWV demands the server to keep taking vacation until it finds at least a single customer waiting in the system at an instant vacation completion. On returning of the server from his vacation along with finding at least one customer in the system, the server changes its service rate, thereby giving rise to a non-vacation period; otherwise the server immediately goes for another WV. We formulate the probability generating function for the number of customers present when the server is both in a service period as well as in a working vacation period. We further derive a closed-form solution for various performance measures such as the mean queue length and the mean waiting time. The stochastic decomposition properties are verified for the model

Performance analysis of a discrete-time queueing system with customer deadlines

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the "deadline" of the customer. Deadlines of consecutive customers are modelled as independent and geometrically distributed random variables. The arrival process of new customers, furthermore, is assumed to be general and independent, while service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for quantities as the mean system content, the mean customer delay, and the deadline-expiration ratio. These formulas, however, contain infinite sums and infinite products, which implies that truncations are required to actually compute numerical values. Therefore, we also derive some easy-to-evaluate approximate results for the main performance measures. These approximate results are quite accurate, as we show in some numerical examples. Possible applications of this type of queueing model are numerous: the (variable) deadlines could model, for instance, the fact that customers may become impatient and leave the queue unserved if they have to wait too long in line, but they could also reflect the fact that the service of a customer is not useful anymore if it cannot be delivered soon enough, etc