The Conditional Distribution of Waiting Time Given Queue Length
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Dipak D. Patil
Abstract
In this paper we propose a conditional distribution of the waiting time given the queue length. We assume that the number of customers in a queue, that is the queue length, follows a geometric distribution and the waiting time of a newly arrived customer in a queue follows an exponential distribution. We model the conditional distribution of the waiting time given the queue length using Gumbel's bivariate exponential copula. Parameters are estimated using the likelihood approach with a two stage estimation procedure. A simulation study indicates the performance of the estimators. Asymptotic properties of the estimators of the parameters are studied. We apply the model to a real data set to illustrate the dependence between the waiting time and the queue length.
©2014 Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Acceptance Sampling Plans for Percentiles Assuming the Linear Failure Rate Distribution
- The Conditional Distribution of Waiting Time Given Queue Length
- Posterior Control Chart for Process Average under Conjugate Prior Distribution
- Bayesian Reliability Sampling Plans under the Conditions of Rayleigh-Inverse-Rayleigh Distribution
- Inferences of the Lifetime Performance Index with Lomax Distribution Based on Progressive Type-II Censored Data
- Acceptance Sampling Plan Based on Truncated Life Tests for Three Parameter Kappa Distribution
- Bhattacharrya and Kshirsagar Lower Bounds for the Natural Exponential Family (NEF)
- A Note on a Generalization of the Exponentiated Pareto Distribution
Articles in the same Issue
- Frontmatter
- Acceptance Sampling Plans for Percentiles Assuming the Linear Failure Rate Distribution
- The Conditional Distribution of Waiting Time Given Queue Length
- Posterior Control Chart for Process Average under Conjugate Prior Distribution
- Bayesian Reliability Sampling Plans under the Conditions of Rayleigh-Inverse-Rayleigh Distribution
- Inferences of the Lifetime Performance Index with Lomax Distribution Based on Progressive Type-II Censored Data
- Acceptance Sampling Plan Based on Truncated Life Tests for Three Parameter Kappa Distribution
- Bhattacharrya and Kshirsagar Lower Bounds for the Natural Exponential Family (NEF)
- A Note on a Generalization of the Exponentiated Pareto Distribution
