Non-Equilibrium Statistical Physics of Currents in Queuing Networks

We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition rates between nodes. For such systems, we ask the question ``What is the most likely way for large currents to accumulate over time in a network ?'', where time is large compared to the system correlation time scale. We identify two interesting regimes. In the first regime, in which the accumulation of currents over time exceeds the expected value by a small to moderate amount (moderate large deviation), we find that the large-deviation distribution of currents is universal (independent of the interaction details), and there is no long-time and averaged over time accumulation of particles (condensation) at any nodes. In the second regime, in which the accumulation of currents over time exceeds the expected value by a large amount (severe large deviation), we find that the large-deviation current distribution is sensitive to interaction details, and there is a long-time accumulation of particles (condensation) at some nodes. The transition between the two regimes can be described as a dynamical second order phase transition. We illustrate these ideas using the simple, yet non-trivial, example of a single node with feedback.Comment: 26 pages, 5 figure

A Kriging Method for Modeling Cycle Time-Throughput Profiles in Manufacturing

In semiconductor manufacturing, the steady-state behavior of a wafer fab system can be characterized by its cycle time-throughput profiles. These profiles quantify the relationship between the cycle time of a product and the system throughput and product mix. The objective of this work is to efficiently generate such cycle time-throughput profiles in manufacturing which can further assist decision makings in production planning.;In this research, a metamodeling approach based on Stochastic Kriging model with Qualitative factors (SKQ) has been adopted to quantify the target relationship of interest. Furthermore, a sequential experimental design procedure is developed to improve the efficiency of simulation experiments. For the initial design, a Sequential Conditional Maximin algorithm is utilized. Regarding the follow-up designs, batches of design points are determined using a Particle Swarm Optimization algorithm.;The procedure is applied to a Jackson network, as well as a scale-down wafer fab system. In both examples, the prediction performance of the SKQ model is promising. It is also shown that the SKQ model provides narrower confidence intervals compared to the Stochastic Kriging model (SK) by pooling the information of the qualitative variables

On Coding for Reliable Communication over Packet Networks

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks.Comment: 33 pages, 6 figures; revised appendi

Modeling the Emergency Care Delivery System Using a Queueing Approach

This thesis considers a regional emergency care delivery system that has a common emergency medical service (EMS) provider and two hospitals, each with a single emergency department (ED) and an inpatient department (ID). Patients arrive at one of the hospital EDs either by ambulance or self-transportation, and we assume that an ambulance patient has preemptive priority over a walk-in patient. Both types of patients can potentially be admitted into the ID or discharged directly from the ED. An admitted patient who cannot access the ID due to the lack of available inpatient beds becomes a boarding patient and blocks an ED server. An ED goes on diversion, e.g., requests the EMS provider to divert incoming ambulances to the neighboring facility, if the total number of its ambulance patients and boarding patients exceeds its capacity (the total number of its servers). The EMS provider will accept the diversion request if the neighboring ED is not on diversion. Both EDs choose its capacity as its diversion threshold and never change the threshold value strategically, and hence they never game. Although the network could be an idealized model of an actual operation, it can be thought of as the simplest network model that is rich enough to reproduce the variety of interactions among different system components. In particular, we aim to highlight the bottleneck effect of inpatient units on ED overcrowding and the network effects resulting from ED diversions. A continuous time Markov chain is introduced for the network model. We show that the chain is irreversible and hence its stationary distribution is difficult to characterize analytically. We identify an alternative solution that builds on queueing decomposition and matrix-analytic methods. We demonstrate through discrete-event simulations the effectiveness of this solution on deriving various performance measures of the original network model. Moreover, by conducting extensive numerical experiments, we provide potential explanations for the overcrowding and delays in a network of hospitals. We suggest remedies from a queueing perspective for the operational challenges facing emergency care delivery systems

Joint rate control and scheduling for providing bounded delay with high efficiency in multihop wireless networks

This thesis considers the problem of supporting traffic with elastic bandwidth requirements and hard end-to-end delay constraints in multi-hop wireless networks, with focus on source transmission rates and link data rates as the key resource allocation decisions. Specifically, the research objective is to develop a source rate control and scheduling strategy that guarantees bounded average end-to-end queueing delay and maximises the overall utility of all incoming traffic, using network utility maximisation framework. The network utility maximisation based approaches to support delay-sensitive traffic have been predominantly based on either reducing link utilisation, or approximation of links as M/D/1 queues. Both approaches lead to unpredictable transient behaviour of packet delays, and inefficient link utilisation under optimal resource allocation. On the contrary, in this thesis an approach is proposed where instead of hard delay constraints based on inaccurate M/D/1 delay estimates, traffic end-to-end delay requirements are guaranteed by proper forms of concave and increasing utility functions of their transmission rates. Specifically, an alternative formulation is presented where the delay constraint is omitted and sources’ utility functions are multiplied by a weight factor. The alternative optimisation problem is solved by a distributed scheduling algorithm incorporating a duality-based rate control algorithm at its inner layer, where optimal link prices correlate with their average queueing delays. The proposed approach is then realised by a scheduling algorithm that runs jointly with an integral controller whereby each source regulates the queueing delay on its paths at the desired level, using its utility weight coefficient as the control variable. Since the proposed algorithms are based on solving the alternative concave optimisation problem, they are simple, distributed and lead to maximal link utilisation. Hence, they avoid the limitations of the previous approaches. The proposed algorithms are shown, using both theoretical analysis and simulation, to achieve asymptotic regulation of end-to-end delay given the step size of the proposed integral controller is within a specified range

Concurrent cell rate simulation of ATM telecommunications network.

PhDAbstract not availabl

Statistical multiplexing and connection admission control in ATM networks

Asynchronous Transfer Mode (ATM) technology is widely employed for the transport of network traffic, and has the potential to be the base technology for the next generation of global communications. Connection Admission Control (CAC) is the effective traffic control mechanism which is necessary in ATM networks in order to avoid possible congestion at each network node and to achieve the Quality-of-Service (QoS) requested by each connection. CAC determines whether or not the network should accept a new connection. A new connection will only be accepted if the network has sufficient resources to meet its QoS requirements without affecting the QoS commitments already made by the network for existing connections. The design of a high-performance CAC is based on an in-depth understanding of the statistical characteristics of the traffic sources