Impatient Customers in an Markovian Queue with Bernoulli Schedule Working Vacation Interruption and Setup Time

In this paper, using probability generating function method, Impatient customers in an Markovian queue with Bernoulli schedule working vacation interruption and setup time is discussed. Customers impatience is due to the servers vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular service period with probability (1 - b) or continues the vacation with probability b. We obtain the probability generating functions of the stationary state probabilities, performance measures, sojourn time of a customer and stochastic decomposition of the queue length, waiting time and numerical results

Analysis of an M/G/1 queue with customer impatience and an adaptive arrival process

We study an M/G/1 queue with impatience and an adaptive arrival process. The rate of the arrival process changes according to whether an incoming customer is accepted or rejected. We analyse two different models for impatience : (i) based on workload, and (ii) based on queue length. For the workload-based model, we obtain the Laplace-Stieltjes Transform of the joint stationary workload and arrival rate process, and that of the waiting time. For the queue-length based model we obtain the analogous z-transform. These queueing models also capture the interaction between congestion control algorithms and queue management schemes in the Internet

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