In this paper we discuss the problem of change point for the interarrival time distribution in th... more In this paper we discuss the problem of change point for the interarrival time distribution in the context of exponential families for the queueing system. We consider the problem of detecting an influential point concerning change-point using Bayes factors. Numerical examples are simulated using Monte Carlo methods for various sample sizes of the arriving customers at different positions of change based on the Erlang distribution
Abstract Although queueing models in the mathematical field of queueing theory are mainly studied... more Abstract Although queueing models in the mathematical field of queueing theory are mainly studied in the steady-state regime and practical applications are interested mostly in queues in transient situations subject to burst arrivals and congestion, their use is still justified as a first step towards a more complex and thorough analysis. In these practical applications, parameters such as the traffic intensity, which is the ratio between the arrival rate and service rate, are unknown and need to be estimated statistically. In this study, a Markovian arrival and deterministic single-server queueing system, known in Kendall notation as an M ∕ D ∕ 1 queueing model, is considered. This is one of the simplest queueing models with deterministic service time and may be seen as an approximation of a variety of applications in the performance evaluation of production management, telecommunications networks, and other areas. The main goal of this manuscript is to propose a methodology to determine the sample size for an M ∕ D ∕ 1 queueing system under the Bayesian setup by observing the number of customer arrivals during the service time of a customer. To verify the efficiency and efficacy of the proposed approach, an extensive set of numerical results is presented and discussed.
The paper is concerned with the problem of change point for the inter arrival time distribution f... more 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 $$(\rho _1)$$ ( ρ 1 ) and after the change $$(\rho _2)$$ ( ρ 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.
Journal of Computational and Applied Mathematics, 2021
Abstract A certain type of queueing system that is quite common in manufacturing systems occurs w... more Abstract 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.
In this paper we discuss the problem of change point for the interarrival time distribution in th... more In this paper we discuss the problem of change point for the interarrival time distribution in the context of exponential families for the queueing system. We consider the problem of detecting an influential point concerning change-point using Bayes factors. Numerical examples are simulated using Monte Carlo methods for various sample sizes of the arriving customers at different positions of change based on the Erlang distribution
Abstract Although queueing models in the mathematical field of queueing theory are mainly studied... more Abstract Although queueing models in the mathematical field of queueing theory are mainly studied in the steady-state regime and practical applications are interested mostly in queues in transient situations subject to burst arrivals and congestion, their use is still justified as a first step towards a more complex and thorough analysis. In these practical applications, parameters such as the traffic intensity, which is the ratio between the arrival rate and service rate, are unknown and need to be estimated statistically. In this study, a Markovian arrival and deterministic single-server queueing system, known in Kendall notation as an M ∕ D ∕ 1 queueing model, is considered. This is one of the simplest queueing models with deterministic service time and may be seen as an approximation of a variety of applications in the performance evaluation of production management, telecommunications networks, and other areas. The main goal of this manuscript is to propose a methodology to determine the sample size for an M ∕ D ∕ 1 queueing system under the Bayesian setup by observing the number of customer arrivals during the service time of a customer. To verify the efficiency and efficacy of the proposed approach, an extensive set of numerical results is presented and discussed.
The paper is concerned with the problem of change point for the inter arrival time distribution f... more 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 $$(\rho _1)$$ ( ρ 1 ) and after the change $$(\rho _2)$$ ( ρ 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.
Journal of Computational and Applied Mathematics, 2021
Abstract A certain type of queueing system that is quite common in manufacturing systems occurs w... more Abstract 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.
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Papers by saroja kumar singh