Approximation for single-channel multi-server queues and queuing networks with generally distributed inter-arrival and service times

This dissertation is divided into two papers. The first paper is related to developing a closed-form approximation for single-channel multiple-server queues with generally distributed inter-arrival and service times, which are often found in numerous settings, e.g., airports and manufacturing systems. Unfortunately, exact models for such systems require distributions for the underlying random variables. Further, data for fitting distributions is sometimes not available, and one only has access to means and variances of the underlying input random variables. Under heavy traffic, excellent approximations already exist for this purpose. In the first paper, a new approximation method for medium traffic is presented. Encouraging numerical evidence for gamma distributed inter-arrival times, often found in many settings, and double-tapering distributions, such as normal, triangular, and gamma, for the service time, is found with the new approximation. In the second paper, a new approximation technique is studied for modeling a two-stage queueing network (QN) in which the first stage contains a multiple-server (G/G/k) queue and the second is composed of multiple single-server queues (G/G/1) in parallel. Airport terminals and other service areas, such as sports stadiums and manufacturing systems, are examples of systems where such two-stage QNs are encountered. The new approximation is rooted in approximating the variance of the service time in a G/G/k queue and leads to encouraging numerical behavior --Abstract, page iv

QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements

AbstractWorkload measurements in enterprise systems often lead to observe a dependence between the number of requests running at a resource and their mean service requirements. However, multiclass performance models that feature these dependences are challenging to analyze, a fact that discourages practitioners from characterizing workload dependences. We here focus on closed multiclass queueing networks and introduce QD-AMVA, the first approximate mean-value analysis (AMVA) algorithm that can efficiently and robustly analyze queue-dependent service times in a multiclass setting. A key feature of QD-AMVA is that it operates on mean values, avoiding the computation of state probabilities. This property is an innovative result for state-dependent models, which increases the computational efficiency and numerical robustness of their evaluation. Extensive validation on random examples, a cloud load-balancing case study and comparison with a fluid method and an existing AMVA approximation prove that QD-AMVA is efficient, robust and easy to apply, thus enhancing the tractability of queue-dependent models

Deep Reinforcement Learning Models for Real-Time Traffic Signal Optimization with Big Traffic Data

One of the most significant changes that the globe has faced in recent years is the changes brought about by the COVID19 pandemic. While this research was started before the pandemic began, the pandemic has exposed the value that data and information can have in modern society. During the pandemic traffic volumes changed substantially, leaving the inefficiencies of existing methods exposed. This research has focussed on exploring two key ideas that will become increasingly relevant as societies adapt to these changes: Big Data and Artificial Intelligence. For many municipalities, traffic signals are still re-timed using traditional approaches and there is still significant reliance on static timing plans designed with data collected from static field studies. This research explored the possibility of using travel-time data obtained from Bluetooth and WiFi sniffing. Bluetooth and WiFi sniffing is an emerging Big Data approach that takes advantage of the ability to track and monitor unique devices as they move from location to location. An approach to re-time signals using an adaptive system was developed, analysed, and tested under varying conditions. The results of this work showed that this data could be used to improve delays by as much as 10\% when compared to traditional approaches. More importantly, this approach demonstrated that it is possible to re-time signals using a readily available and dynamic data source without the need for field volume studies. In addition to Big Data technologies, Artificial Intelligence (AI) is increasingly playing an important role in modern technologies. AI is already being used to make complex decisions, categorise images, and can best humans in complex strategy games. While AI shows promise, applications to Traffic Engineering have been limtied. This research has advanced the state-of-the art by conducting a systematic sensitivity study on an AI technique, Deep Reinforcement Learning. This thesis investigated and identified optimal settings for key parameters such as the discount factor, learning rate, and reward functions. This thesis also developed and tested a complete framework that could potentially be applied to evaluate AI techniques in field settings. This includes applications of AI techniques such as transfer learning to reduce training times. Finally, this thesis also examined framings for multi-intersection control, including comparisons to existing state-of-the art approaches such as SCOOT

Queues with waiting time dependent service

Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples. © 2011 The Author(s)