Queue methods for variability in congested traffic

Time-dependent queue methods are extended to calculate variances of stochastic queues along with their means, and thereby provide a tool for evaluation and better understanding of travel time variability and reliability in congested traffic networks and other systems, including through probability distributions estimated from moments. Objectives include developing computationally efficient analytical methods, and achieving robustness by reflecting the underlying structure of queuing systems rather than relying on statistical fitting, New deterministic and equilibrium formulae for queue variance are developed, acting also as constraints on estimating time-dependent queues generated by a range of processes, enabling improved accuracy and reliability estimates. New methods for approximating equilibrium and dynamic probability distributions use respectively doubly-nested geometric distributions and exponentially-weighted combinations of exponential and Normal functions, avoiding the need to rely on empirical functions, costly simulation, or equilibrium distributions inappropriate in dynamic cases. For growing queues, corrections are made to the popular sheared approximation, that combines deterministic and Pollaczek-Khinchin equilibrium mean formulae in one time-dependent function. For decaying queues, a new exponential approximation is found to give better results, possibly through avoiding implicit quasi-static assumption in shearing. Predictions for M/M/1 (yield) and M/D/1 (signal) processes applied to 34 oversaturated peaks show good agreement when tested against Markov simulations based on recurrence relations. Looking to widen the range of queues amenable to time-dependent methods, dependence of stochastic signal queues on green period capacity is confirmed by an extended M/D/1 process, for which new formulae for equilibrium moments are obtained and compared with earlier approximations. A simple formulation of queuing on multiple lanes with shared service is developed, two-lane examples with turning movements showing fair match to simulation. The main new methods are implemented in a spreadsheet demonstrator program, incorporating a database of time-sliced peak cases together with a procedure for estimating dynamic probability distributions from moments

A unified method to analyze overtake free queueing systems

Includes bibliographical references (p. 51-52).Supported by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118 Supported by the National Science Foundation. DDM-9014751Dimitris Bertsimas and Georgia Mourtzinou

Dynamic Vehicle Routing for Data Gathering in Wireless Networks

We consider a dynamic vehicle routing problem in wireless networks where messages arriving randomly in time and space are collected by a mobile receiver (vehicle or a collector). The collector is responsible for receiving these messages via wireless communication by dynamically adjusting its position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the delay performance in such networks. We show that the necessary and sufficient condition for the stability of such a system (in the bounded average number of messages sense) is given by {\rho}<1 where {\rho} is the average system load. We derive fundamental lower bounds for the delay in the system and develop policies that are stable for all loads {\rho}<1 and that have asymptotically optimal delay scaling. Furthermore, we extend our analysis to the case of multiple collectors in the network. We show that the combination of mobility and wireless transmission results in a delay scaling of {\Theta}(1/(1- {\rho})) with the system load {\rho} that is a factor of {\Theta}(1/(1- {\rho})) smaller than the delay scaling in the corresponding system where the collector visits each message location.Comment: 19 pages, 7 figure

PERFORMANCE LIMITS FOR ENERGY-CONSTRAINED COMMUNICATION SYSTEMS

Ph.DDOCTOR OF PHILOSOPH

Standard and retrial queueing systems: a comparative analysis

We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.)leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type and multiserver M/M/c type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, ossess unique distinguished features. We also mention some open problems.We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.)leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type and multiserver M/M/c type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, ossess unique distinguished features. We also mention some open problems

Insensitive Bounds for the Stationary Distribution of a Single Server Retrial Queue with Server Subject to Active Breakdowns

The paper addresses monotonicity properties of the single server retrial queue with no waiting room and server subject to active breakdowns. The obtained results allow us to place in a prominent position the insensitive bounds for the stationary distribution of the embedded Markov chain related to the model in the study. Numerical illustrations are provided to support the results