Jan-Kees C. W. van Ommeren

A new approximation algorithm for the multilevel facility location problem

In this paper we propose a new integer programming formulation for the multilevel facility location problem and a novel 3-approximation algorithm based on LP-rounding. The linear program that we use has a polynomial number of variables and constraints, thus being more efficient than the one commonly used in the approximation algorithms for these types of problems.

A Tandem Queueing Model for Delay Analysis in Disconnected Ad Hoc Networks

Ad hoc network routing protocols may fail to operate in the absence of an end-to-end connection from source to destination. This deficiency can be resolved by so-called delay-tolerant networking which exploits the mobility of the nodes by letting them operate as relays according to the store-carry-and-forward paradigm. In this work, we analyze the delay performance of a small mobile ad hoc network by considering a tandem queueing system. We present an exact packet-level analysis by applying ideas from the polling literature. Due to the state-space expansion, this analysis cannot efficiently be applied for all model parameter settings. For this reason, an analytical approximation is constructed and its excellent performance has extensively been validated. Numerical results on the mean end-to-end delay show that the switch-over time distribution impacts this metric only through its first two moments. Finally, we study delay optimization under power control.

The Remaining Service Time upon Reaching a High Level in M/G/1 Queues

The distribution of the remaining service time upon reaching some target level in an M/G/1 queue is of theoretical as well as practical interest. In general, this distribution depends on the initial level as well as on the target level, say, B. Two initial levels are of particular interest, namely, level “1” (i.e., upon arrival to an empty system) and level “B−1” (i.e., upon departure at the target level).In this paper, we consider a busy cycle and show that the remaining service time distribution, upon reaching a high level B due to an arrival, converges to a limiting distribution for B→∞. We determine this asymptotic distribution upon the “first hit” (i.e., starting with an arrival to an empty system) and upon “subsequent hits” (i.e., starting with a departure at the target) into a high target level B. The form of the limiting (asymptotic) distribution of the remaining service time depends on whether the system is stable or not. The asymptotic analysis in this paper also enables us to obtain good analytical approximations of interesting quantities associated with rare events, such as overflow probabilities.

A polling model with an autonomous server

This paper considers polling systems with an autonomous server that remains at a queue for an exponential amount of time before moving to a next queue incurring a generally distributed switch-over time. The server remains at a queue until the exponential visit time expires, also when the queue becomes empty. If the queue is not empty when the visit time expires, service is preempted upon server departure, and repeated when the server returns to the queue. The paper first presents a necessary and sufficient condition for stability, and subsequently analyzes the joint queue-length distribution via an embedded Markov chain approach. As the autonomous exponential visit times may seem to result in a system that closely resembles a system of independent queues, we explicitly investigate the approximation of our system via a system of independent vacation queues. This approximation is accurate for short visit times only.

Time-limited polling systems with batch arrivals and phase-type service times

In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling systems. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-lengths at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains.

The impact of interference on optimal multi-path routing in ad hoc networks

We develop a queueing model characterizing explicitly the impact of interference on end-to-end performance measures such as throughput in ad hoc networks, emphasizing the performance trade-off between single-path and multi-path routing. It may seem attractive to employ multi-path routing, but as all nodes share a single channel, efficiency may drop due to increased interference levels thus yielding singlepath performance for some topologies. We formulate a nonlinear programming problem to optimize network performance. Next, we focus on network capacity and show that for this objective the optimum could be found by solving an exponential number of linear programmes. We propose a greedy algorithm that efficiently searches these programmes to approximate the optimal solution. Numerical results for small topologies provide structural insight in optimal path selection and demonstrate the excellent performance of the proposed algorithm. Besides, larger networks and more advanced scenarios with multiple source-destination pairs and different radio ranges are analyzed.

Analytical models to determine room requirements in outpatient clinics

Outpatient clinics traditionally organize processes such that the doctor remains in a consultation room while patients visit for consultation, we call this the Patient-to-Doctor policy (PtD-policy). A different approach is the Doctor-to-Patient policy (DtP-policy), whereby the doctor travels between multiple consultation rooms, in which patients prepare for their consultation. In the latter approach, the doctor saves time by consulting fully prepared patients. We use a queueing theoretic and a discrete-event simulation approach to provide generic models that enable performance evaluations of the two policies for different parameter settings. These models can be used by managers of outpatient clinics to compare the two policies and choose a particular policy when redesigning the patient process. We use the models to analytically show that the DtP-policy is superior to the PtD-policy under the condition that the doctor’s travel time between rooms is lower than the patient’s preparation time. In addition, to calculate the required number of consultation rooms in the DtP-policy, we provide an expression for the fraction of consultations that are in immediate succession; or, in other words, the fraction of time the next patient is prepared and ready, immediately after a doctor finishes a consultation. We apply our methods for a range of distributions and parameters and to a case study in a medium-sized general hospital that inspired this research.

Energy-delay tradeoff in a two-way relay with network coding

A queueing model for a relay in a communication network that is employing network coding is introduced. It is shown that communication networks with coding are closely related to queueing networks with positive and negative customers. The tradeoff between minimizing energy consumption and minimizing delay for a two-way relay is investigated. Analytical upper and lower bounds on the energy consumption and the delay are obtained using a Markov reward approach. Exact expressions are given for the minimum energy consumption and the minimum delay that are attainable.

A Stochastic Model for Interterminal Container Transportation

We propose a novel semiopen queuing network (SOQN) model for the interterminal transportation (ITT) problem where multiple container terminals use a common fleet of vehicles (automated lift vehicles, automated guided vehicles, multitrailers, and barges) to transport containers between terminals. To solve the overall queuing network, our solution approach uses a network decomposition method where the original SOQN is decomposed to a closed and an open queuing network (with bulk-service capacity). To our knowledge, this is the first work that considers bulk service in SOQNs. We develop theoretical upper and lower bounds on the throughput time estimates of our model, and provide an extension for the case when service times at the terminal handling stations depend on the number of containers being loaded/unloaded. We numerically validate our model using simulated data where we find that our model results in errors of less than 5% for vehicle utilization. We also show that our model results in better estimates for the ITT problem when compared to existing approaches in the literature. Finally, we apply our model to real-world data from the Port of Rotterdam and show that it can be used to analyze throughput time trade-offs with alternate dwell point policies, different vehicle types, and variable vehicle capacities.The online appendix is available at https://doi.org/10.1287/trsc.2016.0726 .

A linear programming approach to error bounds for random walks in the quarter-plane

We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities along the boundaries of the state space. A Markov reward approach is used to bound the approximation error. The main contribution of the work is the formulation of a linear program that provides the approximation error.