van der Rob Mei

Revenue Management under Customer Choice Behaviour with Cancellations and Overbooking

In many application areas such as airlines and hotels a large number of bookings are typically cancelled. Explicitly taking into account cancellations creates an opportunity for increasing revenue. Motivated by this we propose a revenue management model based on Talluri and van Ryzin (2004) that takes cancellations into account in addition to customer choice behaviour. Moreover, we consider overbooking limits as these are influenced by cancellations. We model the problem as a Markov decision process and propose three dynamic programming formulations to solve the problem, each appropriate in a different setting. We show that in certain settings the problem can be solved exactly using a tractable solution method. For other settings we propose tractable heuristics, since the problem faces the curse of dimensionality. Numerical results show that the heuristics perform almost as good as the exact solution. However, the model without cancellations can lead to a revenue loss of up to 20 percent. Lastly we provide a parameter estimation method based on Newman et al. (2014). This estimation method is fast and provides good parameter estimates. The combination of the model, the tractable and well-performing solution methods, and the parameter estimation method ensures that the model can efficiently be applied in practice.

Effective load for flow-level performance modelling of file transfers in wireless LANs

Today, a wide range of 802.11-based Wireless LANs (WLANs) have become dominant to provide wireless Internet access for file transfers. For engineering purposes, there is a need for very simple, explicit, yet accurate, models that predict the performance of WLANs under anticipated load conditions. In this context, several detailed packet-level models have been proposed, based on fixed-point equations. Despite the fact that these models generally lead to accurate performance predictions, they do not lead to simple explicit expressions for the performance of WLANs. Motivated by this, we propose a new analytic model that captures the highly complex combined dynamics and protocol overhead of the 802.11 MAC, IP, TCP and application-layer into an explicit expression for a single parameter which will be called the effective service time. Based on the effective service time, we define the effective load to describe the flow-level performance of file transfers over WLANs with an M/G/1 Processor Sharing (PS) model. Using the M/G/1 PS model properties we propose a simple analytic model to obtain WLAN AP buffer content distribution. Despite the fact that PS models are heavily used in modelling flow-level performance in communication networks, an extensive validation of such models has not been published in the field, or context, of WLAN. To this end, our model is validated extensively by comparing the model-based average response times against simulations. The results show that the model leads to highly accurate predictions over a wide range of parameter combinations, including light- and heavy-tailed file-size distributions and light- and heavy-load scenarios. The simplicity and accuracy of the model make the results of high practical relevance and useful for performance engineering purposes.

A dynamic ambulance management model for rural areas

We study the Dynamic Ambulance Management (DAM) problem in which one tries to retain the ability to respond to possible future requests quickly when ambulances become busy. To this end, we need models for relocation actions for idle ambulances that incorporate different performance measures related to response times. We focus on rural regions with a limited number of ambulances. We model the region of interest as an equidistant graph and we take into account the current status of both the system and the ambulances in a state. We do not require ambulances to return to a base station: they are allowed to idle at any node. This brings forth a high degree of complexity of the state space. Therefore, we present a heuristic approach to compute redeployment actions. We construct several scenarios that may occur one time-step later and combine these scenarios with each feasible action to obtain a classification of actions. We show that on most performance indicators, the heuristic policy significantly outperforms the classical compliance table policy often used in practice.

Optimal Job Splitting in Parallel Processor Sharing Queues

The main barrier to the sustained growth of wireless communications is the Shannon limit that applies to the channel capacity. A promising means to realize high-capacity enhancements is the use of multi-path communication solutions to improve reliability and network performance in areas that are covered by a multitude of overlapping wireless access networks. Despite the enormous potential for capacity enhancements offered by multi-path communication techniques, little is known about how to effectively exploit this. Motivated by this, we study a model where jobs are split and downloaded over N multiple parallel networks, each of which is modeled as a processor sharing (PS) queue. Each job is fragmented, according to a fixed splitting rule and re-assembled at the receiving end. The complex correlation structure between the sojourn times at the PS nodes makes an exact detailed mathematical analysis of the model impossible. Therefore, in this article we propose a simple and fast approximation for the splitting rule that minimizes the expected job-download time. Our approximation is validated extensively by simulations. The results show that the outcomes are extremely accurate over a wide range of parameter combinations.

Statistical Properties of Task Running Times in a Global-Scale Grid Environment

Grid computing technology connects globally distributed processors to develop an immense source of computing power, which enables us to run applications in parallel that would take orders of magnitude more time on a single processor. Key characteristics of a global-scale grid are the strong burstiness in the amount of load on the resources and on the network capacities, and the fact that processors may be appended to or removed from the grid at any time. To cope with these characteristics, it is essential to develop techniques that make applications robust against the dynamics of the grid environment. For these techniques to be effective, it is important to have an understanding of the statistical properties of the dynamics of a grid environment. Today, however, the statistical properties of the dynamic behavior of real global-scale grid environments are not well understood. Our main focus is on highly CPU-intensive grid applications that require huge amounts of processor power for running tasks. Motivated by this, we have performed extensive measurements in a real, global-scale grid environment to study the statistical properties of the running times of tasks on processors. We observe (1) a strong burstiness of the running times over different time scales, (2) a strong heterogeneity of the running-time characteristics among the different hosts, (3) a strong heterogeneity of the running-time characteristics for the same host over different time intervals, and (4) the occurrence of sudden level-switches in the running times, amongst others. These observations are used to develop effective techniques for the prediction of running times. They can be used to develop effective control schemes for robust grid applications.

Rate stability and output rates in queueing networks with shared resources

Motivated by a variety of applications in information and communication systems, we consider queueing networks in which the service rate at each of the individual nodes depends on the state of the entire system. The behavior of these types of networks is fundamentally different from classical queueing networks, where the service rate at each queue is usually assumed to be independent of the state of the other nodes. We study the per-queue rate stability and output rates for a class of networks with a general capacity allocation function. More specifically, we derive necessary conditions for per-queue rate stability, and give bounds for the per-node output rate and asymptotic growth rates, under mild assumptions on the allocation function. For a set of parallel queues, we further prove the convergence of the output rates (for almost all input parameters) to easily computable values and we give a sharp characterization of the per-queue rate stability. The results provide new intuition and fundamental insight into the stability and throughput behavior of queueing networks with shared resources.

Sojourn time approximations in queueing networks with feedback

This paper is motivated by the response-time analysis of distributed information systems, where transactions are handled by a sequence of front-end server and back-end server actions. We study sojourn times in an open queueing network with a single Processor Sharing (PS) node and an arbitrary number of M multi-server First-Come-First-Served (FCFS) nodes. Customers arrive at the PS according to a Poisson process. After departing from the PS node a customer jumps to FCFS node k with probability pk, and departs from the system with probability 1 - p, where p = Σk-1M pk (0 < p < 1). After receiving service at a FCFS node, a customer jumps back to the PS node. For this model, we focus on the mean and the variability of the sojourn time of an arbitrary customer in the system. The model is a product-form network, which immediately leads to a closed-form expression for the mean sojourn times. The variance of the sojourn times, however, does not admit an exact expression; the complexity is caused by the possibility of overtaking. To this end, we propose a new methodology for deriving closed-form approximations for the variance of sojourn times in queueing networks with feedback. Numerical results from extensive experimentation with simulations demonstrates that the approximations are highly accurate for a wide range of parameter values.

The effect of ambulance relocations on the performance of ambulance service providers

Dynamic Ambulance Management (DAM) is generally believed to provide means to enhance the response-time performance of emergency medical service providers. The implementation of DAM algorithms leads to additional movements of ambulance vehicles compared to the reactive paradigm, where ambulances depart from the base station when an incident is reported. In practice, proactive relocations are only acceptable when the number of additional movements is limited. Motivated by this trade-off, we study the effect of the number of relocations on the response-time performance. We formulate the relocations from one configuration to a target configuration by the Linear Bottleneck Assignment Problem, so as to provide the quickest way to transition to the target configuration. Moreover, the performance is measured by a general penalty function, assigning to each possible response time a certain penalty. We extensively validate the effectiveness of relocations for a wide variety of realistic scenarios, including a day and night scenario in a critically and realistically loaded system. The results consistently show that already a small number of relocations lead to near-optimal performance, which is important for the implementation of DAM algorithms in practice.

On the estimation of the true demand in call centers with redials and reconnects

In practice, in many call centers customers often perform redials (i.e., reattempt after an abandonment) and reconnects (i.e., reattempt after an answered call). In the literature, call center models usually do not cover these features, while real data analysis and simulation results show ignoring them inevitably leads to inaccurate estimation of the total inbound volume. Therefore, in this paper we propose a performance model that includes both features. In our model, the total volume consists of three types of calls: (1) fresh calls (i.e., initial call attempts), (2) redials, and (3) reconnects. In practice, the total volume is used to make forecasts, while according to the simulation results, this could lead to high forecast errors, and subsequently wrong staffing decisions. However, most of the call center data sets do not have customer-identity information, which makes it difficult to identify how many calls are fresh and what fractions of the calls are redials and reconnects.

Dynamic ambulance dispatching:is the closest-idle policy always optimal?

We address the problem of ambulance dispatching, in which we must decide which ambulance to send to an incident in real time. In practice, it is commonly believed that the ‘closest idle ambulance’ rule is near-optimal and it is used throughout most literature. In this paper, we present alternatives to the classical closest idle ambulance rule. Most ambulance providers as well as researchers focus on minimizing the fraction of arrivals later than a certain threshold time, and we show that significant improvements can be obtained by our alternative policies. The first alternative is based on a Markov decision problem (MDP), that models more than just the number of idle vehicles, while remaining computationally tractable for reasonably-sized ambulance fleets. Second, we propose a heuristic for ambulance dispatching that can handle regions with large numbers of ambulances. Our main focus is on minimizing the fraction of arrivals later than a certain threshold time, but we show that with a small adaptation our MDP can also be used to minimize the average response time. We evaluate our policies by simulating a large emergency medical services region in the Netherlands. For this region, we show that our heuristic reduces the fraction of late arrivals by 18 % compared to the ‘closest idle’ benchmark policy. A drawback is that this heuristic increases the average response time (for this problem instance with 37 %). Therefore, we do not claim that our heuristic is practically preferable over the closest-idle method. However, our result sheds new light on the popular belief that the closest idle dispatch policy is near-optimal when minimizing the fraction of late arrivals.