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The paper is concerned with the problem of change point for the inter arrival time distribution for the M/M/1 queueing system by considering the number of customers present in the system. Bayesian estimators of traffic intensities, before the change $$(\rho _1)$$ and after the change $$(\rho _2)$$ , and the change point m are derived using the informative as well as non-informative priors under different loss functions. Finally a numerical example along with a practical example is given to illustrate the results.

The paper discusses the rate of convergence in the Bernstein–von Mises theorem for M/M/1 queueing system which is observed over a continuous time interval (0, T] where T is a suitable stopping time.

In this paper, we prove the Bernstein-von Mises theorem for the GI∕G∕1 queueing system which is observed over a continuous time interval (0, T], where T is a suitable stopping time. And also the as...

Very often it is impracticable or costly to collect all information regarding the arrival times and service times of queue. In such a situation, it is therefore necessary to develop sampling plans ...

Let θ be the unknown parameter for the arrival process in a single M/M/1 queue. The paper discusses the bound for the equivalence of Bayes and maximum likelihood estimator for the parameter...

In this paper, we study the change point problem for the $$M/E_r/1$$ queueing system. Bayesian estimators of parameter and the change point are derived under different loss functions using both the informative (beta prior) and non-informative priors (Jeffreys prior). Also empirical Bayes procedure is used to compute the parameters. Simulation and data analysis on real life are given to illustrate the results.

Problems of large sample estimation for the parameters in a single server queueing set up are discussed. The queueing system is observed over a continuous time interval (0,T] , where T is determined by a suitable stopping rule. The asymptotic properties of the maximum likelihood estimator from single server queues are studied using the martingale technique. An example with simulation study is given to illustrate the results.

The paper deals with the asymptotic joint posterior distribution of $$(\theta , \phi )$$ in a GI / G / 1 queueing system over a continuous time interval (0, T] where $$\theta $$ and $$\phi $$ are unknown parameters of arrival process and departure process respectively and T is a suitable stopping time.

A certain type of queueing system that is quite common in manufacturing systems occurs when the time between the arrivals of items approximately follows an exponential distribution with rate λ , the services are mechanized and their times may be considered approximately constant ( b ). In Kendall notation, such a queueing system is well known as an M ∕ D ∕ 1 queue; despite being one of the simplest queueing models, it has wide applicability to numerous practical situations as a first approximation by a steady-state model before a deeper analysis can be performed by means of more sophisticated transient-regime stochastic models that consider, for example, burst arrival, block arrivals, congestion, and so on. In queues, one very important parameter that must estimated is the traffic intensity, defined for an M ∕ D ∕ 1 queue as ρ = λ b . This article aims to investigate statistical methods to estimate ρ , namely, the maximum likelihood and Bayes estimators, by considering the number of customers present in the system at successive departure epochs, which is a very natural way to collect data. An extensive set of computational results from Monte Carlo simulations is shown to establish the efficiency and effectiveness of the proposed approaches, which will possibly enhance practical applications.

The paper is concerned with the study of change point problem in the inter-arrival time and service time of single server queues. Maximum likelihood estimators of the parameters are derived. A test statistics has been developed and its properties have been studied.

The article deals with Bernstein–von Mises theorem, for the arrival process in a M | M |1 queue.

This paper presents the derivation of maximum likelihood estimates for the arrival rate and service rates in a stationary M/M/c queue with heterogeneous servers. Although previous works facing the problem can be found in the literature, all of them are only valid under the assumption of transferring of customers in service. A more realistic approach for many systems is developed in this paper. This model considers the customers are attended by the available faster server and there is no transfer of customers among servers. The model can be applied in a large variety of systems such as production systems, banking, cyber cafe or taxi station.

The paper is concerned with the maximum likelihood estimation of the change point of arrival rate for an M/M/1/m queueing system. It is assumed that the change takes place after a fixed unknown number of completed services. We also calculate the maximum likelihood estimators of the traffic intensities after and before the change point and we prove that these estimators are weakly consistent. This work is applicable in planning economic models, social events and service to customers, where the service rate changes due to fatigue of the server or there is a shift change policy after a fixed amount of services done.