Probabilistic maximal covering location-allocation models with constrained waiting time or queue length for congested systems

When dealing with the design of service networks, such as healthand EMS services, banking or distributed ticket selling services, thelocation of service centers has a strong influence on the congestion ateach of them, and consequently, on the quality of service. In this paper,several models are presented to consider service congestion. The firstmodel addresses the issue of the location of the least number of single--servercenters such that all the population is served within a standard distance,and nobody stands in line for a time longer than a given time--limit, or withmore than a predetermined number of other clients. We then formulateseveral maximal coverage models, with one or more servers per service center.A new heuristic is developed to solve the models and tested in a 30--nodesnetwork.

Queue Length Simulations in a Finite Single-line Queueing System with Repeated Calls

2000 Mathematics Subject Classification: 60K25.

Weak Ergodicity of Mt /Mt /N /N + R Queue

2000 Mathematics Subject Classification: 60J27, 60K25.

Evaluation of Variable Advisory Speed Limits in Work Zones, TPF-5(081), 2013

Variable advisory speed limit (VASL) systems could be effective at both urban and rural work zones, at both uncongested and congested sites. At uncongested urban work zones, the average speeds with VASL were lower than without VASL. But the standard deviation of speeds with VASL was higher. The increase in standard deviation may be due to the advisory nature of VASL. The speed limit compliance with VASL was about eight times greater than without VASL. At the congested sites, the VASL were effective in making drivers slow down gradually as they approached the work zone, reducing any sudden changes in speeds. Mobility-wise the use of VASL resulted in a decrease in average queue length, throughput, number of stops, and an increase in travel time. Several surrogate safety measures also demonstrated the benefits of VASL in congested work zones. VASL deployments in rural work zones resulted in reductions in mean speed, speed variance, and 85th percentile speeds downstream of the VASL sign. The study makes the following recommendations based on the case studies investigated: 1. The use of VASL is recommended for uncongested work zones to achieve better speed compliance and lower speeds. Greater enforcement of regulatory speed limits could help to decrease the standard deviation in speeds; 2. The use of VASL to complement the static speed limits in rural work zones is beneficial even if the VASL is only used to display the static speed limits. It leads to safer traffic conditions by encouraging traffic to slow down gradually and by reminding traffic of the reduced speed limit. A well-designed VASL algorithm, like the P5 algorithm developed in this study, can significantly improve the mobility and safety conditions in congested work zones. The use of simulation is recommended for optimizing the VASL algorithms before field deployment.

Effectiveness of Work Zone Intelligent Transportation Systems, TPF-5(081), 2013

In the last decade, Intelligent Transportation Systems (ITS) have increasingly been deployed in work zones by state departments of transportation. Also known as smart work zone systems they improve traffic operations and safety by providing real-time information to travelers, monitoring traffic conditions, and managing incidents. Although there have been numerous ITS deployments in work zones, a framework for evaluating the effectiveness of these deployments does not exist. To justify the continued development and implementation of smart work zone systems, this study developed a framework to determine ITS effectiveness for specific work zone projects. The framework recommends using one or more of five performance measures: diversion rate, delay time, queue length, crash frequency, and speed. The monetary benefits and costs of ITS deployment in a work zone can then be computed using the performance measure values. Such ITS computations include additional considerations that are typically not present in standard benefit-cost computations. The proposed framework will allow for consistency in performance measures across different ITS studies thus allowing for comparisons across studies or for meta analysis. In addition, guidance on the circumstances under which ITS deployment is recommended for a work zone is provided. The framework was illustrated using two case studies: one urban work zone on I-70 and one rural work zone on I-44, in Missouri. The goals of the two ITS deployments were different – the I-70 ITS deployment was targeted at improving mobility whereas the I-44 deployment was targeted at improving safety. For the I-70 site, only permanent ITS equipment that was already in place was used for the project and no temporary ITS equipment was deployed. The permanent DMS equipment serves multiple purposes, and it is arguable whether that cost should be attributed to the work zone project. The data collection effort for the I-70 site was very significant as portable surveillance captured the actual diversion flows to alternative routes. The benefit-cost ratio for the I-70 site was 2.1 to 1 if adjusted equipment costs were included and 6.9 to 1 without equipment costs. The safety-focused I-44 ITS deployment had an estimated benefit-cost ratio of 3.2 to 1.

Effects of Road Construction Intensity and Operations on Rural Freeway Work Zone Capacity, TPF-5(081), 2014

Capacity is affected by construction type and its intensity on adjacent open traffic lanes. The effect on capacity is a function of vehicles moving in and out of the closed lanes of the work zone, and the presence of heavy construction vehicles. Construction activity and its intensity, however, are not commonly considered in estimating capacity of a highway lane. The main purpose of this project was to attempt to quantify the effects of construction type and intensity (e.g. maintenance, rehabilitation, reconstruction, and milling) on work zone capacity. The objective of this project is to quantify the effects of construction type and its intensity on work zone capacity and to develop guidelines for MoDOT to estimate the specific operation type and intensity that will improve the traffic flow by reducing the traffic flow and queue length commonly associated with work zones. Despite the effort put into field data collection, the data collected did not show a full speed-flow chart therefore extracting a reliable capacity value was difficult. A statistical comparison between the capacity values found in this study using either methodologies indicates that there is an effect of construction activity on the values work zone capacity. It was found that the heavy construction activity reduces the capacity. It is very beneficial to conduct similar studies on the capacity of work zone with different lane closure barriers, which is also directly related to the type of work zone being short-term or long-term work zones. Also, the effect of different geometric and environmental characteristics of the roadway should be considered in future studies.

Behavioural queueing : cellular automata and a laboratory experiment

Dans cette thèse, nous étudions les aspects comportementaux d'agents qui interagissent dans des systèmes de files d'attente à l'aide de modèles de simulation et de méthodologies expérimentales. Chaque période les clients doivent choisir un prestataire de servivce. L'objectif est d'analyser l'impact des décisions des clients et des prestataires sur la formation des files d'attente. Dans un premier cas nous considérons des clients ayant un certain degré d'aversion au risque. Sur la base de leur perception de l'attente moyenne et de la variabilité de cette attente, ils forment une estimation de la limite supérieure de l'attente chez chacun des prestataires. Chaque période, ils choisissent le prestataire pour lequel cette estimation est la plus basse. Nos résultats indiquent qu'il n'y a pas de relation monotone entre le degré d'aversion au risque et la performance globale. En effet, une population de clients ayant un degré d'aversion au risque intermédiaire encoure généralement une attente moyenne plus élevée qu'une population d'agents indifférents au risque ou très averses au risque. Ensuite, nous incorporons les décisions des prestataires en leur permettant d'ajuster leur capacité de service sur la base de leur perception de la fréquence moyenne d'arrivées. Les résultats montrent que le comportement des clients et les décisions des prestataires présentent une forte "dépendance au sentier". En outre, nous montrons que les décisions des prestataires font converger l'attente moyenne pondérée vers l'attente de référence du marché. Finalement, une expérience de laboratoire dans laquelle des sujets jouent le rôle de prestataire de service nous a permis de conclure que les délais d'installation et de démantèlement de capacité affectent de manière significative la performance et les décisions des sujets. En particulier, les décisions du prestataire, sont influencées par ses commandes en carnet, sa capacité de service actuellement disponible et les décisions d'ajustement de capacité qu'il a prises, mais pas encore implémentées. - Queuing is a fact of life that we witness daily. We all have had the experience of waiting in line for some reason and we also know that it is an annoying situation. As the adage says "time is money"; this is perhaps the best way of stating what queuing problems mean for customers. Human beings are not very tolerant, but they are even less so when having to wait in line for service. Banks, roads, post offices and restaurants are just some examples where people must wait for service. Studies of queuing phenomena have typically addressed the optimisation of performance measures (e.g. average waiting time, queue length and server utilisation rates) and the analysis of equilibrium solutions. The individual behaviour of the agents involved in queueing systems and their decision making process have received little attention. Although this work has been useful to improve the efficiency of many queueing systems, or to design new processes in social and physical systems, it has only provided us with a limited ability to explain the behaviour observed in many real queues. In this dissertation we differ from this traditional research by analysing how the agents involved in the system make decisions instead of focusing on optimising performance measures or analysing an equilibrium solution. This dissertation builds on and extends the framework proposed by van Ackere and Larsen (2004) and van Ackere et al. (2010). We focus on studying behavioural aspects in queueing systems and incorporate this still underdeveloped framework into the operations management field. In the first chapter of this thesis we provide a general introduction to the area, as well as an overview of the results. In Chapters 2 and 3, we use Cellular Automata (CA) to model service systems where captive interacting customers must decide each period which facility to join for service. They base this decision on their expectations of sojourn times. Each period, customers use new information (their most recent experience and that of their best performing neighbour) to form expectations of sojourn time at the different facilities. Customers update their expectations using an adaptive expectations process to combine their memory and their new information. We label "conservative" those customers who give more weight to their memory than to the xiv Summary new information. In contrast, when they give more weight to new information, we call them "reactive". In Chapter 2, we consider customers with different degree of risk-aversion who take into account uncertainty. They choose which facility to join based on an estimated upper-bound of the sojourn time which they compute using their perceptions of the average sojourn time and the level of uncertainty. We assume the same exogenous service capacity for all facilities, which remains constant throughout. We first analyse the collective behaviour generated by the customers' decisions. We show that the system achieves low weighted average sojourn times when the collective behaviour results in neighbourhoods of customers loyal to a facility and the customers are approximately equally split among all facilities. The lowest weighted average sojourn time is achieved when exactly the same number of customers patronises each facility, implying that they do not wish to switch facility. In this case, the system has achieved the Nash equilibrium. We show that there is a non-monotonic relationship between the degree of risk-aversion and system performance. Customers with an intermediate degree of riskaversion typically achieve higher sojourn times; in particular they rarely achieve the Nash equilibrium. Risk-neutral customers have the highest probability of achieving the Nash Equilibrium. Chapter 3 considers a service system similar to the previous one but with risk-neutral customers, and relaxes the assumption of exogenous service rates. In this sense, we model a queueing system with endogenous service rates by enabling managers to adjust the service capacity of the facilities. We assume that managers do so based on their perceptions of the arrival rates and use the same principle of adaptive expectations to model these perceptions. We consider service systems in which the managers' decisions take time to be implemented. Managers are characterised by a profile which is determined by the speed at which they update their perceptions, the speed at which they take decisions, and how coherent they are when accounting for their previous decisions still to be implemented when taking their next decision. We find that the managers' decisions exhibit a strong path-dependence: owing to the initial conditions of the model, the facilities of managers with identical profiles can evolve completely differently. In some cases the system becomes "locked-in" into a monopoly or duopoly situation. The competition between managers causes the weighted average sojourn time of the system to converge to the exogenous benchmark value which they use to estimate their desired capacity. Concerning the managers' profile, we found that the more conservative Summary xv a manager is regarding new information, the larger the market share his facility achieves. Additionally, the faster he takes decisions, the higher the probability that he achieves a monopoly position. In Chapter 4 we consider a one-server queueing system with non-captive customers. We carry out an experiment aimed at analysing the way human subjects, taking on the role of the manager, take decisions in a laboratory regarding the capacity of a service facility. We adapt the model proposed by van Ackere et al (2010). This model relaxes the assumption of a captive market and allows current customers to decide whether or not to use the facility. Additionally the facility also has potential customers who currently do not patronise it, but might consider doing so in the future. We identify three groups of subjects whose decisions cause similar behavioural patterns. These groups are labelled: gradual investors, lumpy investors, and random investor. Using an autocorrelation analysis of the subjects' decisions, we illustrate that these decisions are positively correlated to the decisions taken one period early. Subsequently we formulate a heuristic to model the decision rule considered by subjects in the laboratory. We found that this decision rule fits very well for those subjects who gradually adjust capacity, but it does not capture the behaviour of the subjects of the other two groups. In Chapter 5 we summarise the results and provide suggestions for further work. Our main contribution is the use of simulation and experimental methodologies to explain the collective behaviour generated by customers' and managers' decisions in queueing systems as well as the analysis of the individual behaviour of these agents. In this way, we differ from the typical literature related to queueing systems which focuses on optimising performance measures and the analysis of equilibrium solutions. Our work can be seen as a first step towards understanding the interaction between customer behaviour and the capacity adjustment process in queueing systems. This framework is still in its early stages and accordingly there is a large potential for further work that spans several research topics. Interesting extensions to this work include incorporating other characteristics of queueing systems which affect the customers' experience (e.g. balking, reneging and jockeying); providing customers and managers with additional information to take their decisions (e.g. service price, quality, customers' profile); analysing different decision rules and studying other characteristics which determine the profile of customers and managers.

Queueing Models with Vacations and Working Vacations

The thesis entitled “Queueing Models with Vacations and Working Vacations" consists of seven chapters including the introductory chapter. In chapters 2 to 7 we analyze different queueing models highlighting the role played by vacations and working vacations. The duration of vacation is exponentially distributed in all these models and multiple vacation policy is followed.In chapter 2 we discuss an M/M/2 queueing system with heterogeneous servers, one of which is always available while the other goes on vacation in the absence of customers waiting for service. Conditional stochastic decomposition of queue length is derived. An illustrative example is provided to study the effect of the input parameters on the system performance measures. Chapter 3 considers a similar setup as chapter 2. The model is analyzed in essentially the same way as in chapter 2 and a numerical example is provided to bring out the qualitative nature of the model. The MAP is a tractable class of point process which is in general nonrenewal. In spite of its versatility it is highly tractable as well. Phase type distributions are ideally suited for applying matrix analytic methods. In all the remaining chapters we assume the arrival process to be MAP and service process to be phase type. In chapter 4 we consider a MAP/PH/1 queue with working vacations. At a departure epoch, the server finding the system empty, takes a vacation. A customer arriving during a vacation will be served but at a lower rate.Chapter 5 discusses a MAP/PH/1 retrial queueing system with working vacations.In chapter 6 the setup of the model is similar to that of chapter 5. The signicant dierence in this model is that there is a nite buer for arrivals.Chapter 7 considers an MMAP(2)/PH/1 queueing model with a nite retrial group

Queueing Models with Vacations and Working Vacations

The objective of the study of \Queueing models with vacations and working vacations" was two fold; to minimize the server idle time and improve the e ciency of the service system. Keeping this in mind we considered queueing models in di erent set up in this thesis. Chapter 1 introduced the concepts and techniques used in the thesis and also provided a summary of the work done. In chapter 2 we considered an M=M=2 queueing model, where one of the two heterogeneous servers takes multiple vacations. We studied the performance of the system with the help of busy period analysis and computation of mean waiting time of a customer in the stationary regime. Conditional stochastic decomposition of queue length was derived. To improve the e ciency of this system we came up with a modi ed model in chapter 3. In this model the vacationing server attends the customers, during vacation at a slower service rate. Chapter 4 analyzed a working vacation queueing model in a more general set up. The introduction of N policy makes this MAP=PH=1 model di erent from all working vacation models available in the literature. A detailed analysis of performance of the model was provided with the help of computation of measures such as mean waiting time of a customer who gets service in normal mode and vacation mode.

An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

Analysis of computer communication systems by use of digital signal processing methods

Queueing theory is an effective tool in the analysis of canputer camrunication systems. Many results in queueing analysis have teen derived in the form of Laplace and z-transform expressions. Accurate inversion of these transforms is very important in the study of computer systems, but the inversion is very often difficult. In this thesis, methods for solving some of these queueing problems, by use of digital signal processing techniques, are presented. The z-transform of the queue length distribution for the Mj GY jl system is derived. Two numerical methods for the inversion of the transfom, together with the standard numerical technique for solving transforms with multiple queue-state dependence, are presented. Bilinear and Poisson transform sequences are presented as useful ways of representing continuous-time functions in numerical computations.

Generalized Priority Systems. Analytical Results and Numerical Algorithms

A class of priority systems with non-zero switching times, referred as generalized priority systems, is considered. Analytical results regarding the distribution of busy periods, queue lengths and various auxiliary characteristics are presented. These results can be viewed as generalizations of the Kendall functional equation and the Pollaczek-Khintchin transform equation, respectively. Numerical algorithms for systems’ busy periods and traffic coefficients are developed. ACM Computing Classification System (1998): 60K25.

Predicting delay reductions from freeway traffic diversion for incident management

Traffic incidents are a major source of traffic congestion on freeways. Freeway traffic diversion using pre-planned alternate routes has been used as a strategy to reduce traffic delays due to major traffic incidents. However, it is not always beneficial to divert traffic when an incident occurs. Route diversion may adversely impact traffic on the alternate routes and may not result in an overall benefit. This dissertation research attempts to apply Artificial Neural Network (ANN) and Support Vector Regression (SVR) techniques to predict the percent of delay reduction from route diversion to help determine whether traffic should be diverted under given conditions. The DYNASMART-P mesoscopic traffic simulation model was applied to generate simulated data that were used to develop the ANN and SVR models. A sample network that comes with the DYNASMART-P package was used as the base simulation network. A combination of different levels of incident duration, capacity lost, percent of drivers diverted, VMS (variable message sign) messaging duration, and network congestion was simulated to represent different incident scenarios. The resulting percent of delay reduction, average speed, and queue length from each scenario were extracted from the simulation output. The ANN and SVR models were then calibrated for percent of delay reduction as a function of all of the simulated input and output variables. The results show that both the calibrated ANN and SVR models, when applied to the same location used to generate the calibration data, were able to predict delay reduction with a relatively high accuracy in terms of mean square error (MSE) and regression correlation. It was also found that the performance of the ANN model was superior to that of the SVR model. Likewise, when the models were applied to a new location, only the ANN model could produce comparatively good delay reduction predictions under high network congestion level.

Efficient asynchronous scheduling algorithms for cost-effective buffered crossbar switches

Buffered crossbar switches have recently attracted considerable attention as the next generation of high speed interconnects. They are a special type of crossbar switches with an exclusive buffer at each crosspoint of the crossbar. They demonstrate unique advantages over traditional unbuffered crossbar switches, such as high throughput, low latency, and asynchronous packet scheduling. However, since crosspoint buffers are expensive on-chip memories, it is desired that each crosspoint has only a small buffer. This dissertation proposes a series of practical algorithms and techniques for efficient packet scheduling for buffered crossbar switches. To reduce the hardware cost of such switches and make them scalable, we considered partially buffered crossbars, whose crosspoint buffers can be of an arbitrarily small size. Firstly, we introduced a hybrid scheme called Packet-mode Asynchronous Scheduling Algorithm (PASA) to schedule best effort traffic. PASA combines the features of both distributed and centralized scheduling algorithms and can directly handle variable length packets without Segmentation And Reassembly (SAR). We showed by theoretical analysis that it achieves 100% throughput for any admissible traffic in a crossbar with a speedup of two. Moreover, outputs in PASA have a large probability to avoid the more time-consuming centralized scheduling process, and thus make fast scheduling decisions. Secondly, we proposed the Fair Asynchronous Segment Scheduling (FASS) algorithm to handle guaranteed performance traffic with explicit flow rates. FASS reduces the crosspoint buffer size by dividing packets into shorter segments before transmission. It also provides tight constant performance guarantees by emulating the ideal Generalized Processor Sharing (GPS) model. Furthermore, FASS requires no speedup for the crossbar, lowering the hardware cost and improving the switch capacity. Thirdly, we presented a bandwidth allocation scheme called Queue Length Proportional (QLP) to apply FASS to best effort traffic. QLP dynamically obtains a feasible bandwidth allocation matrix based on the queue length information, and thus assists the crossbar switch to be more work-conserving. The feasibility and stability of QLP were proved, no matter whether the traffic distribution is uniform or non-uniform. Hence, based on bandwidth allocation of QLP, FASS can also achieve 100% throughput for best effort traffic in a crossbar without speedup.

Predicting delay reductions from freeway traffic diversion for incident management

Traffic incidents are a major source of traffic congestion on freeways. Freeway traffic diversion using pre-planned alternate routes has been used as a strategy to reduce traffic delays due to major traffic incidents. However, it is not always beneficial to divert traffic when an incident occurs. Route diversion may adversely impact traffic on the alternate routes and may not result in an overall benefit. This dissertation research attempts to apply Artificial Neural Network (ANN) and Support Vector Regression (SVR) techniques to predict the percent of delay reduction from route diversion to help determine whether traffic should be diverted under given conditions. The DYNASMART-P mesoscopic traffic simulation model was applied to generate simulated data that were used to develop the ANN and SVR models. A sample network that comes with the DYNASMART-P package was used as the base simulation network. A combination of different levels of incident duration, capacity lost, percent of drivers diverted, VMS (variable message sign) messaging duration, and network congestion was simulated to represent different incident scenarios. The resulting percent of delay reduction, average speed, and queue length from each scenario were extracted from the simulation output. The ANN and SVR models were then calibrated for percent of delay reduction as a function of all of the simulated input and output variables. The results show that both the calibrated ANN and SVR models, when applied to the same location used to generate the calibration data, were able to predict delay reduction with a relatively high accuracy in terms of mean square error (MSE) and regression correlation. It was also found that the performance of the ANN model was superior to that of the SVR model. Likewise, when the models were applied to a new location, only the ANN model could produce comparatively good delay reduction predictions under high network congestion level.