Queueing Models and Service Management

Customer Balking Behaviors in a Multi-server Queue with Synchronous Multiple Uninterrupted Vacations Under N-policy

Wei Sun — 2025-12-23

This paper studies the customers’ equilibrium and socially optimal balking behaviors in an M/M/c queue with synchronous multiple uninterrupted vacations under N-policy. Considering four cases where the information about the system is entirely/nearly observable or nearly/entirely unobservable, we obtain and compare the customers’ equilibrium and socially optimal balking strategies, set the pricing strategies and analyze the system manager’s benefits, respectively. It is shown that the pricing strategy varies under different information levels. What’s more, regardless of the information level, the best N-policy should be designed for social optimization. However, when the threshold N is pre-determined, disclosing the information of the servers’ status to customers is a better choice no matter the queue length is observable or not.

The Law of Large Numbers and Central Limit Theorem for Non-Stationary Markov Jump Processes Exhibiting Time-of-Day Effects

Monte Fischer — 2025-12-23

In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in service operations and manufacturing applications in which time-of-day, day-of-week, and secular effects are of first-order importance in predicting system behavior. Our theorems allow for non-stationary reward environments that continuously accumulate reward, while also including contributions from non-stationary lump-sum rewards of random size that are collected at either jump times of the underlying process, jump times of a Poisson process modulated by the underlying process, or scheduled deterministic times. As part of our development, we also obtain a new central limit theorem for the special case in which the jump process transition rates and reward structure are periodic (as may occur over a weekly time interval), as well as for jump process models with resetting. We include a simulation study illustrating the quality of our CLT approximations for several non-stationary stochastic models.

A Case Study on Optimizing Call Center Daily Staff Scheduling Using the Set Covering Model

Xiaodong Liu — 2025-12-23

Efficient staff scheduling in call centers improves operational efficiency, reduces costs, and ensures sufficient customer service. This study addresses the daily shift scheduling problem in a call center with multiple types of tasks. While the set covering model is widely used to derive optimal solutions for such problems, its application requires enumerating all possible combinations of timeslots and tasks. This process significantly increases the complexity of the model, leading to computational difficulties. Additionally, the call center considered in this study permits staff to perform two different types of tasks simultaneously within the same timeslot, which are referred to as pair tasks. This further exacerbates computational challenges, as it significantly increases the number of task pattern combinations, making the model even more difficult to solve.
To address the challenge of exponential growth in combinations, a heuristic algorithm is proposed that not only supports pair tasks within the same timeslot but also significantly reduces the number of task pattern combinations. The algorithm is first applied to the base model (Model 1) to obtain an initial near-optimal solution; then task patterns are refined to further improve solution quality. Subsequently, we augment Model 1 by incorporating real-world operational conditions, yielding Model 2 that better reflects practical requirements. Numerical experiments demonstrate the effectiveness and practicality of the proposed algorithm and models.