M.A.A. Boon

Mixed gated/exhaustive service in a polling model with priorities

In this paper we consider a single-server polling system with switch-over times. We introduce a new service discipline, mixed gated/exhaustive service, that can be used for queues with two types of customers: high and low priority customers. At the beginning of a visit of the server to such a queue, a gate is set behind all customers. High priority customers receive priority in the sense that they are always served before any low priority customers. But high priority customers have a second advantage over low priority customers. Low priority customers are served according to the gated service discipline, i.e. only customers standing in front of the gate are served during this visit. In contrast, high priority customers arriving during the visit period of the queue are allowed to pass the gate and all low priority customers before the gate.We study the cycle time distribution, the waiting time distributions for each customer type, the joint queue length distribution of all priority classes at all queues at polling epochs, and the steady-state marginal queue length distributions for each customer type. Through numerical examples we illustrate that the mixed gated/exhaustive service discipline can significantly decrease waiting times of high priority jobs. In many cases there is a minimal negative impact on the waiting times of low priority customers but, remarkably, it turns out that in polling systems with larger switch-over times there can be even a positive impact on the waiting times of low priority customers.

Delays at signalized intersections with exhaustive traffic control

In this paper, we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting distributions of the delays under heavy traffic (HT) conditions. Furthermore, we derive the light traffic (LT) limit of the mean delays for intersections with Poisson arrivals, and develop a heuristic adaptation of this limit to capture the LT behavior for other interarrival-time distributions. We combine the LT and HT results to develop closed-form approximations for the mean delays of vehicles in each lane. These closed-form approximations are quite accurate, very insightful, and simple to implement.

Queues with skill based parallel servers and a FCFS infinite matching model

We consider the following skill based parallel service queue-ing system: Customers are of types C = {c1,. .. , cI }, servers are of types S = {s1,. .. , sJ }, and there is a bipartite graph G of compatiblities between C, S. The graph has arc (i, j) ∈ G if server type sj has the skill to serve customer type ci. Customers arrive in independent Poisson streams of rates λi, and have absolutely continuous patience distributions Fi. There are nj servers of type sj, and the service times are customer-server-type dependent, the service of a customer of type ci by a server of type sj has a random duration distributed as Gij, with average mij. We use the terminology of queueing theory throughout, but this type of system, with minor modifications, is useful in modeling call centers, manufacturing systems, organ transplants, multimedia servers, and cloud computing [8]. Performance of such systems is highly dependent on the operating policy. We focus here on first come first served (FCFS), where a server is assigned to the longest waiting compatible customer, coupled with assign longest idle server (ALIS), where a customer is assigned to the compatible server that has been idle for the longest time. FCFS-ALIS is widely used, because it is fair to both customers and servers, it is simple to implement, it requires little information about the parameters and the current state of the system, and it is robust under time varying conditions. Our goal here is to develop a structured method to support the design and efficient operation of skill based parallel service systems under FCFS. At this level of generality such systems are highly intractable, no analytic results are expected , and asymptotics, e.g. using many server scaling are called for [12, 10, 7, 13]. We suggest an approximation based on a simplified look at the process — if we discard all arrival *

Statlab: An interactive teaching tool for DOE

An interactive web based teaching tool, Statlab, for Design of Experiments is presented. In this tool, the student is introduced to practical strategies for experimenting through virtual case studies. Statlab forces students to think about practical details since it hides options that students do not ask for. Engineering students as well as industrial participants in our courses consider Statlab as a stimulating learning environment. Statlab can be freely used through the web site www.win.tue.nl/statlab/.

Design heuristic for parallel many server systems

Abstract We study a parallel queueing system with multiple types of servers and customers. A bipartite graph describes which pairs of customer-server types are compatible. We consider the service policy that always assigns servers to the first, longest waiting compatible customer, and that always assigns customers to the longest idle compatible server if on arrival multiple compatible servers are available. For a general renewal stream of arriving customers, general service time distributions that depend both on customer and on server types, and general customer patience distributions, the behavior of such systems is very complicated. Key quantities for their performance are the matching rates, the fraction of services for each pair of compatible customer-server. Calculation of these matching rates in general is intractable, it depends on the entire shape of service time distributions. We suggest through a heuristic argument that if the number of servers becomes large, the matching rates are well approximated by matching rates calculated from the tractable bipartite infinite matching model. We present simulation evidence to support this heuristic argument, and show how this can be used to design systems with desired performance requirements.

Congestion analysis of unsignalized intersections: The impact of impatience and Markov platooning

This paper considers an unsignalized intersection used by two traffic streams. A stream of cars is using a primary road, and has priority over the other stream. Cars belonging to the latter stream cross the primary road if the gaps between two subsequent cars on the primary road are larger than their critical headways. A question that naturally arises relates to the capacity of the secondary road: given the arrival pattern of cars on the primary road, what is the maximum arrival rate of low-priority cars that can be sustained? This paper addresses this issue by considering a compact model that sheds light on the dynamics of the considered unsignalized intersection. The model, which is of a queueing-theoretic nature, reveals interesting insights into the impact of the user behavior on stability. The contributions of this paper are threefold. First, we obtain new results for the aforementioned model that includes driver impatience. Secondly, we reveal some surprising aspects that have remained unobserved in the existing literature so far, many of which are caused by the fact that the capacity of the minor road cannot be expressed in terms of the \emph{mean} gap size; instead more detailed characteristics of the critical headway distribution play a crucial role. The third contribution is the introduction of a new form of bunching on the main road, called Markov platooning. The tractability of this model allows us to study the impact of various platoon formations on the main road on the capacity of the minor road.

Critically loaded k-limited polling systems

We consider a two-queue polling model with switch-over times and

Visualizing multiple quantile plots

k

A polling model with multiple priority levels

-limited service (serve at most

Queue-length balance equations in multiclass multiserver queues and their generalizations

k_i