Queueing Models and Service Management

Stochastic Fluid Flows with Upward Jumps and Phase Transitions: Analysis Through Matrix-Analytic Methods

Barbara Margolius — 2026-03-26

We consider a stochastic fluid model {(X(t), J(t)) : t ≥ 0} with level variable
X(t) ≥ 0, phase variable J(t) and some fixed ‘jump’ levels q_N > . . . > q₁ > 0. The
process is driven by a continuous-time Markov chain {J(t) : t ≥ 0} with state space S,
generator T, and real-valued fluid rates c_i ∈ R for all i ∈ S. The evolution of the level
variable X(t) is such that dX(t)/dt = c_J(t) whenever X(t) > 0, and as soon as the process
hits X(t) = 0, the phase variable J(t) transitions to some phase in S, while the level
variable X(t) may jump to some level q_n > 0, remain at the boundary q₀ = 0 or reflect
from it, and a phase transition may also occur. The process was previously analysed using
various algebraic methods in a special case with N = 1 and without special behaviour at the
boundary q₀. Here, for the first time, we analyse this process using matrix-analytic methods,
which is a powerful methodology in the field of applied probability, suitable for convenient
numerical analysis. We present methodology for the computation of the stationary and transient
distribution of the key performance measures of the model under general assumptions
and illustrate the theory with numerical examples.

Queuing-Inventory System with Attraction-Retention Mechanisms Under a Partial Synchronous Vacation Policy: The Case of Ethio Telecom Service Center in Arba Minch, Ethiopia

Berhanu Mekonen Alemu — 2026-03-26

Quality of service (QoS) is a critical factor for customer satisfaction and operational
efficiency, particularly in service-driven organizations such as Ethio Telecom in
Ethiopia. To address congestion and customer impatience, this study investigates a finitecapacity
multi-server Markovian queuing-inventory system (MQIS) that explicitly incorporates
attraction-retention mechanisms alongside C removable servers operating under a
partial synchronous vacation policy. The attraction-retention strategies are modeled to influence
customer arrival rates and patience levels by encouraging customers to remain in
the system through incentives or improved service quality, thereby mitigating balking and
reneging behaviors. In this setting, any D servers (0 < D < C) may take simultaneous
vacations as a group when no customers are waiting at a service completion epoch, while
the remaining C − D servers continue to operate, either actively serving or idling depending
on the inventory status. Both service and vacation times are exponentially distributed,
and inventory is managed using a continuous-review (q,Q) policy that replenishes stock to
level Q once it drops to q. A continuous-time Markov process is formulated to analyze the
system and steady-state probabilities are derived to evaluate performance measures. To minimize
the total cost, a cost-loss model is proposed and solved using a genetic algorithm to
determine the optimal service rate and the number of servers allocated for vacation. Numerical
experiments based on primary data collected from Ethio Telecom’s Arba Minch branch
demonstrate how attraction-retention mechanisms, along with other system parameters, impact
optimal policies and cost metrics. The proposed model is applicable to a wide range of
service environments, including supermarkets, telecom centers, hospitals, production systems
and restaurants, and can be extended to incorporate batch service, customer retrials, or
catastrophic events.

Editorial: Queueing Models and Service Management — Integrating Theory, Practice, and Innovation

Zhe George Zhang — 2026-03-26

As a Co-Editor-in-Chief, I am pleased to introduce our esteemed contributors, authors, and readers to Queueing Models and Service Management (QMSM), a journal dedicated to publishing rigorous, relevant, and impactful research that advances both the theory and application of queueing models in modern service systems.
Queueing theory has long provided a fundamental analytical framework for understanding congestion, delay, and resource allocation in service systems. Since the early foundational work on stochastic service processes, queueing models have evolved into a rich body of theory encompassing single-server systems, multi-server and many-server models, networks, priority systems, and queueing systems under time-varying environments. Core results such as Little’s Law and heavy-traffic approximations remain central to both theoretical research and practical performance evaluation.
Within the scholarly landscape, journals in operations research and applied probability have played a central role in advancing the theoretical foundations of queueing. Through their emphasis on probabilistic modeling, mathematical structure, and analytical rigor, this body of work has shaped the intellectual development of the field and continues to inspire new theoretical directions. This strong theoretical tradition has provided essential tools and insights for understanding stochastic service systems and remains a cornerstone of ongoing research in queueing.
At the same time, service systems have grown increasingly complex and diverse. Healthcare delivery, call centers, transportation systems, logistics platforms, cloud computing, and digital services all operate under uncertainty, variability, and congestion—conditions that naturally call for queueing-based analysis. In these settings, however, decision-makers are not only interested in theoretical properties of models but also in how queueing insights can inform service design, staffing, capacity planning, and operational control.
It is in this broader context that Queueing Models and Service Management (QMSM) defines its mission.