Queueing Models and Service Management

On Various Age and Residual Life Distributions Associated with the M/G/1 Queue

2024-08-20T14:33:09+00:00

We show how a simple modification of the time-dependent Little’s law can be used to study various types of joint age and residual life distributions associated with any customer waiting in line in equilibrium in a work-conserving M/G/1 queue operating under the first-come-first-served service discipline, not necessarily the customer receiving service. This addresses an open question posed at the end of (Adan and Haviv, Stochastic Models, 2009). We also analyze the joint distribution of the number of customers in the system at time t, the remaining amount of work possessed by the customer currently in service at time t, the amount of work that has already been processed by the customer currently in service at time t, and the amount of time the current customer in service at time t spent waiting in the queue.

Optimization Analysis of Ticket Queues with Balking Customers and Single Vacation Policy

2024-08-20T14:48:17+00:00

Self-checkout services have gained popularity across various industries, offering
Service systems issue numbered tickets for upon arrival customers without physical queues are popularly applied in public sectors. These systems are managed by ticketing technology and thus are different from those in common classical queues. This paper introduces a novel ticket queue that accounts for impatient customers and a single vacation policy. A schematic state-transition-rate diagram with the associated flow-balance equations is presented. The block-partitioned infinitesimal generator is provided in matrix form and the corresponding steady-state probabilities are solved recursively using the matrix-geometric method. We also derive explicit expressions of critical metrics relative to the performance measures. Numerical sensitivity analysis and graphical results are presented to assess the influence of various parameters on system characteristics. To reduce the computational complexity and enhance the analysis efficiency, we simplify the model and provide an efficient approximation method. Furthermore, a stepwise regression model is constructed to estimate the expected number of customers in the system without the need for complex matrix manipulations. Finally, applying the NSGA-II algorithm, a triple-objective optimization problem is investigated to determine the optimal operating condition with the minimum cost.

A Quantitative Model for Staffing Problems in Inpatient Units with Multi-type Patients

2024-08-20T14:59:08+00:00

This paper addresses the staffing problem for inpatient units treating diverse patient types in a hospital. We develop a queueing model to determine the optimal staffing
levels within resource constraints. This quantitative approach offers a valuable analytical
tool for hospital managers, enabling them to make more informed and efficient staffing decisions for inpatient units. To ensure the robustness of the results from our analytical modelin real-world scenarios, we also employ a simulation model. Numerical examples are provided to illustrate the procedure and generate practical insights for healthcare practitioners.