Successful dissertation defense of Ömer Schmiel

On Friday, Febraury 13, 2026, Ömer Schmiel successfully defended his dissertation entitled: “Revisiting the Queue: Empirical, Analytical, and Numerical Insights on Retrials”.

The essays' titles are: “A Survey of Queueing Systems with Retrials”, “Abandon and Return: Empirical Insights into Customer Retrials”, “Stationary Coupled-Flow Approximation for Time-Varying Retrial Queues”, “Déjà Vu on the Line: The Impact of Retrial Time Distribution”.

Congratulations, Ömer!

Abstracts:

A Survey of Queueing Systems with Retrials

Many service operations systems are visited by customers multiple times. This phenomenon is known as retrials. Depending on characteristics of the system or practical motivations, retrials can occur after blocking, reneging, balking, or service. In this work, we give an overview on the literature on retrial queues, reviewing empirical observations, methods for performance evaluations and staffing, and corresponding insights. We identify that exponential distribution may not accurately capture real retrial behavior. However, the majority of the literature on analysis and staffing of retrial queues assumes exponentially distributed retrial times, while only a few studies incorporate generally distribution retrial times. Consequently, our review highlights the need for performance evaluation and staffing approaches that can capture the influence of generally distributed retrial times. 

Abandon and Return: Empirical Insights into Customer Retrials

In call centers, customers may leave the queue before getting service due to a lack of patience, if they face long waiting times. However,  they may re-enter the system after some time as retrials. In this work, we present an empirical analysis of customer retrial patterns in an American call center. 
Therefore, we analyze the distribution of same-day and next-day retrial times and find that, contrary to the common assumption in the call center literature, retrial times are not exponentially distributed. Instead, hyperexponential and gamma distributions provide a better fit to the data and reveal three customer groups characterized by instant, fast, and slow retrials. Further, we identify that both same-day and next-day retrials are influenced by waiting times: longer waiting times result in fewer and slower same-day retrials, but they result in more and faster next-day retrials.  Moreover, we observe that customers who retry the next-day more patient (i.e., are willing to wait longer) than customers who do not retry. On the contrary, customers who retry within the same-day are less patient on their initial try.  Finally, we analyze the time-dependency of retrials and observe that  same-day retrials typically occur shortly after abandonment, whereas next-day retrials usually occur around the call center's opening hour. 

Stationary Coupled-Flow Approximation for Time-Varying Retrial Queues

While stationary queueing models, such as Erlang-C and Erlang-A, are widely used for performance evaluation in service systems, they do not account for time dependency and retrials, which limits their accuracy. This paper addresses this gap by proposing the Stationary Coupled-Flow (SCF) approximation. The method partitions the time horizon into intervals, models each as an M/M/c+G in steady state, and iteratively determines the arrival rate, accounting for new customers and retrials. In this way, we obtain an approximation for long-run performance metrics of retrial queues with stationary and time-varying arrivals. We prove that the SCF approximation converges to a finite limit for constant and cyclic arrival rates. Extensive numerical experiments demonstrate the high accuracy of the SCF approximation. Therefore, SCF provides a fast, transparent tool for planning and staffing in services with retrials. It remains reliable when the exact distribution of retrials is uncertain, enabling day-to-day scheduling and scenario testing under time-varying demand. We identify that the retrial probability plays a stronger role than the retrial time distribution. The impact of retrials in time-varying queues is driven by two effects: the state at the abandonment epoch and the cycle-length–retrial-time interaction. We posit that as retrial times increase, the first effect dampens congestion feedback, whereas the second can amplify or smooth fluctuations. Under sufficiently high variability in retrial times, the cycle-length–retrial-time interaction becomes negligible, leaving the system governed by the abandonment-epoch state.

Déjà Vu on the Line: The Impact of Retrial Time Distribution

Call centers are integral components of modern service systems and serve as primary contact points between companies and their customers. However, their capacity planning poses a challenge due to stochastic and time-dependent demand, as well customer retrials. Although the analysis of retrial queues has been widely studied, the majority considers stationary systems with exponentially distributed retrials, limiting their applicability in call center environments. This work analyzes the impact of retrial probability and retrial time distributions on time-dependent performance measures and staffing decisions using the Stationary Coupled-Flow (SCF) approximation. We prove that an increased retrial probability or faster retrials (in terms of first-order stochastic dominance under a mild condition) results in a larger abandonment probability and throughput, but in a lower throughput of first tryers. As a consequence, less customers are served on their initial try. We numerically demonstrate that the influence of the retrial time distribution on time-dependent performance measures is not restricted to periods of overload, but can persist well beyond the initial demand peak. To analyze the influence of retrials on staffing decisions, we develop a staffing heuristic with interdependent periods (SHIP) for staffing of time-dependent retrial queues with respect to local and global service level constraints (SLCs). We introduce the First-Time Success (FTS) as a SL to prioritize the service of fresh arrivals. We incorporate FTS as a global SLC and show that it can cause an ex-ante anticipation effect, where staffing levels are increased before a demand peak to reduce retrials. Furthermore, we demonstrate that smaller mean retrial times and larger retrial CVs increase total staffing levels significantly, with the effect of retrial CV being especially noticeable when mean retrial time is large.