arXiv subjects

Rob van der Mei

Publications and source records attributed to Rob van der Mei.

24 records · Page 2Linked to original sources

arXiv2019

Dispatching Fire Trucks under Stochastic Driving Times

In this paper we discuss optimal dispatching of fire trucks, based on a particular dispatching problem that arises at the Amsterdam Fire Department, where two fire trucks are send to the same incident location for a quick response. We formulate the dispatching problem as a Markov Decision Process, and numerically obtain the optimal dispatching decisions using policy iteration. We show that the fraction of late arrivals can be significantly reduced by deviating from current practice of dispatching the closest available trucks, with a relative improvement of on average about $20\%$, and over $50\%$ for certain instances. We also show that driving-time correlation has a non-negligible impact on decision making, and if ignored may lead to performance decrease of over $20\%$ in certain cases. As the optimal policy cannot be computed for problems of realistic size due to the computational complexity of the policy iteration algorithm, we propose a dispatching heuristic based on a queueing approximation for the state of the network. We show that the performance of this heuristic is close to the optimal policy, and requires significantly less computational effort.

math.OC↗

arXiv2016

Heavy traffic analysis of roving server networks

This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves the system or is routed to another queue. This type of customer routing in queueing networks arises very naturally in many application areas (in production systems, computer- and communication networks, maintenance, etc.). In these networks, the single most important characteristic of the system performance is oftentimes the path time, i.e. the total time spent in the system by an arbitrary customer traversing a specific path. The current paper presents the first HT asymptotic for the path-time distribution in queueing networks with a roving server under general renewal arrivals. In particular, we provide a strong conjecture for the system's behaviour under HT extending the conjecture of Coffman et al. [E.G. Coffman Jr., A.A. Puhalskii, M.I. Reiman 1995 and 1998] to the roving server setting of the current paper. By combining this result with novel light-traffic asymptotics we derive an approximation of the mean path-time for arbitrary values of the load and renewal arrivals. This approximation is not only highly accurate for a wide range of parameter settings, but is also exact in various limiting cases.

math.PR↗

arXiv2014

Waiting times in queueing networks with a single shared server

We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems, and robotics. Special cases of the introduced network include well-known polling models, tandem queues, systems with a waiting room, multi-stage models with parallel queues, and many others. A complicating factor of this model is that the internally rerouted customers do not arrive at the various queues according to a Poisson process, causing standard techniques to find waiting-time distributions to fail. In this paper we develop a new method to obtain exact expressions for the Laplace-Stieltjes transforms of the steady-state waiting-time distributions. This method can be applied to a wide variety of models which lacked an analysis of the waiting-time distribution until now.

math.PR↗

arXiv2014

Applications of polling systems

Since the first paper on polling systems, written by Mack in 1957, a huge number of papers on this topic has been written. A typical polling system consists of a number of queues, attended by a single server. In several surveys, the most notable ones written by Takagi, detailed and comprehensive descriptions of the mathematical analysis of polling systems are provided. The goal of the present survey paper is to complement these papers by putting the emphasis on \emph{applications} of polling models. We discuss not only the capabilities, but also the limitations of polling models in representing various applications. The present survey is directed at both academicians and practitioners.

math.PR↗

arXiv2014

Queueing networks with a single shared server: light and heavy traffic

We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems and robotics. Special cases of the introduced network include well-known polling models and tandem queues. We derive exact limits of the mean delays under both heavy-traffic and light-traffic conditions. By interpolating between these asymptotic regimes, we develop simple closed-form approximations for the mean delays for arbitrary loads.

math.PR↗

arXiv2013

Fluid Approximation of a Call Center Model with Redials and Reconnects

In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). The combination of redials and reconnects has not been considered when making staffing decisions, while ignoring them will inevitably lead to under- or overestimation of call volumes, which results in improper and hence costly staffing decisions. Motivated by this, in this paper we study call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations for the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such a model is the unique solution to a system of three differential equations. Furthermore, we use the fluid limit to calculate the expected total arrival rate, which is then given as an input to the Erlang A model for the purpose of calculating service levels and abandonment rates. The performance of such a procedure is validated in the case of single intervals as well as multiple intervals with changing parameters.

math.PR↗