Routing in multi-class queueing networks

PhD ThesisWe consider the problem of routing (incorporating local scheduling) in a distributed network. Dedicated jobs arrive directly at their specified station for processing. The choice of station for generic jobs is open. Each job class has an associated holding cost rate. We aim to develop routing policies to minimise the long-run average holding cost rate. We first consider the class of static policies. Dacre, Glazebrook and Nifio-Mora (1999) developed an approach to the formulation of static routing policies, in which the work at each station is scheduled optimally, using the achievable region approach. The achievable region approach attempts to solve stochastic optimisation problems by characterising the space of all possible performances and optimising the performance objective over this space. Optimal local scheduling takes the form of a priority policy. Such static routing policies distribute the generic traffic to the stations via a simple Bernoulli routing mechanism. We provide an overview of the achievements made in following this approach to static routing. In the course of this discussion we expand upon the study of Becker et al. (2000) in which they considered routing to a collection of stations specialised in processing certain job classes and we consider how the composition of the available stations affects the system performance for this particular problem. We conclude our examination of static routing policies with an investigation into a network design problem in which the number of stations available for processing remains to be determined. The second class of policies of interest is the class of dynamic policies. General DP theory asserts the existence of a deterministic, stationary and Markov optimal dynamic policy. However, a full DP solution may be unobtainable and theoretical difficulties posed by simple routing problems suggest that a closed form optimal policy may not be available. This motivates a requirement for good heuristic policies. We consider two approaches to the development of dynamic routing heuristics. We develop an idea proposed, in the context of simple single class systems, by Krishnan (1987) by applying a single policy improvement step to some given static policy. The resulting dynamic policy is shown to be of simple structure and easily computable. We include an investigation into the comparative performance of the dynamic policy with a number of competitor policies and of the performance of the heuristic as the number of stations in the network changes. In our second approach the generic traffic may only access processing when the station has been cleared of all (higher priority) jobs and can be considered as background work. We deploy a prescription of Whittle (1988) developed for RBPs to develop a suitable approach to station indexation. Taking an approximative approach to Whittle's proposal results in a very simple form of index policy for routing the generic traffic. We investigate the closeness to optimality of the index policy and compare the performance of both of the dynamic routing policies developed here

Stability criteria for controlled queueing networks

We give criteria for the stability of a very general queueing model under different levels of control. A complete classification of stability (or positive recurrence), transience and null-recurrence is presented for the two queue model. The stability and instability results are extended for models with N > 3 queues. We look at a broad class of models which can have the following features: Customers arrive at one, several or all of the queues from the outside with exponential inter arrival times. We often have the case where a arrival stream can be routed so that under different routing schemes each queue can have external arrivals, i.e. we assume we have some control over the routing of the arrivals. We also consider models where the arrival streams are fixed. We view the service in a more abstract way, in that we allow a number к of different service configurations. Under every such service configuration service is provided to some or all of the queues, length of service time can change from one service configuration to another and we can change from one configuration to another according two some control policy. The service times are assumed to be exponentially distributed. The queueing models we consider are networks where, after completion at one queue, a customer might be fed back into another queue where it will be served another time often under with a different service time. These feedback probabilities change with the service configurations. Our interest is in different types of control policies which allow us to change the routing of arrivals and configurations of the service from time to time so that the controlled queue length process (which in most cases is Markov) is stable. The semi-martingale or Lyapunov function methods we use give necessary and sufficient conditions for the stability classification. We will look at some two queue models with different inter arrival and service times where the queueing process is still Markov

Resource allocation policies for service provisioning systems

This thesis is concerned with maximising the efficiency of hosting of service provisioning systems consisting of clusters or networks of servers. The tools employed are those of probabilistic modelling, optimization and simulation. First, a system where the servers in a cluster may be switched dynamically and preemptively from one kind of work to another is examined. The demand consists of two job types joining separate queues, with different arrival and service characteristics, and also different relative importance represented by appropriate holding costs. The switching of a server from queue i to queue j incurs a cost which may be monetary or may involve a period of unavail- ability. The optimal switching policy is obtained numerically by solving a dynamic programming equation. Two heuristic policies - one static and one are evaluated by simulation and are compared to the optimal dynamic - policy. The dynamic heuristic is shown to perform well over a range of pa- rameters, including changes in demand. The model, analysis and evaluation are then generalized to an arbitrary number, M, of job types. Next, the problem of how best to structure and control a distributed com- puter system containing many processors is considered. The performance trade-offs associated with different tree structures are evaluated approximately by applying appropriate queueing models. It is shown that. for a given set of parameters and job distribution policy, there is an optimal tree structure that minimizes the overall average response time. This is obtained numerically through comparison of average response times. A simple heuris- tic policy is shown to perform well under certain conditions. The last model addresses the trade-offs between reliability and perfor- mance. A number of servers, each of which goes through alternating periods of being operative and inoperative, offer services to an incoming stream of demands. The objective is to evaluate and optimize performance and cost metrics. A large real-life data set containing information about server break- downs is analyzed first. The results indicate that the durations of the oper- ative periods are not distributed exponentially. However, hyperexponential distributions are found to be a good fit for the observed data. A model based on these distributions is then formulated, and is solved exactly using the method of spectral expansion. A simple approximation which is accu- rate for heavily loaded systems is also proposed. The results of a number of numerical experiments are reported.EThOS - Electronic Theses Online ServiceBritish Telecom, North-East Regional e-Science CentreGBUnited Kingdo

Predicting software performance in symmetric multi-core and multiprocessor Environments

With today\u27s rise of multi-core processors, concurrency becomes a ubiquitous challenge in software development.Performance prediction methods have to reflect the influence of multiprocessing environments on software performance in order to help software architects to find potential performance problems during early development phases. In this thesis, we address the influence of the operating system scheduler on software performance in symmetric multiprocessing environments

Admission Control and Routing in Multi-Priority Systems

We consider a manufacturer that offers two types of prioritized warranties for its product. Type 1 warranty guarantees a shorter turnaround time than type 2 warranty. Hence items covered by type 1 warranty receive higher priority in repair service. When an item under warranty fails, the manufacturer sends it to one of several repair vendors for repair, who are under contracts to provide repair service for the manufacturer. The manufacturer pays each vendor a fixed fee per repair assignment. While an item is at the vendor under or awaiting repair, a linear holding cost is incurred by the vendor and a linear good-will cost is incurred by the manufacturer. We first study the admission control problem for a single vendor that can either accept or reject an incoming repair assignment in order to maximize its own profit. We analyze the optimal control policies under three criteria: individual optimization, class optimization, and social optimization. By exploiting two proof methods, value iteration algorithm and sample path analysis, we prove that the optimal policy under each criterion has switching-curve structure. We also compare the optimal policies under the three criteria mentioned above and show that (i) the class-optimal policy accepts more high priority customers but fewer low priority customers than the socially optimal policy, which has interesting socioeconomic connotation, (ii) the individually optimal policy accepts more high priority customers than the class-optimal policy, while it can accept either more or fewer low-priority customers than either of the other two optimal policies. We then consider the warranty repair allocation problem which the manufacturer faces. The manufacturer's goal is to allocate the repair work in such a way that the total cost (including fixed cost and good-will cost) is minimized. The complexity of the problem makes the attempt to find the optimal policy very unlikely to succeed. Therefore, we turn our attention to heuristic routing procedures. We develop an effective and robust index-based policy by applying a single policy improvement step to a well-chosen static routing policy. We evaluate the index-based policy and compare it with other heuristics via simulation

Optimal Planning of Container Terminal Operations

Due to globalization and international trade, moving goods using a mixture of transportation modes has become a norm; today, large vessels transport 95% of the international cargos. In the first part of this thesis, the emphasis is on the sea-land intermodal transport. The availability of different modes of transportation (rail/road/direct) in sea-land intermodal transport and container flows (import, export, transhipment) through the terminal are considered simultaneously within a given planning time horizon. We have also formulated this problem as an Integer Programming (IP) model and the objective is to minimise storage cost, loading and transportation cost from/to the customers. To further understand the computational complexity and performance of the model, we have randomly generated a large number of test instances for extensive experimentation of the algorithm. Since, CPLEX was unable to find the optimal solution for the large test problems; a heuristic algorithm has been devised based on the original IP model to find near „optimal‟ solutions with a relative error of less than 4%. Furthermore, we developed and implemented Lagrangian Relaxation (LR) of the IP formulation of the original problem. The bounds derived from LR were improved using sub-gradient optimisation and computational results are presented. In the second part of the thesis, we consider the combined problems of container assignment and yard crane (YC) deployment within the container terminal. A new IP formulation has been developed using a unified approach with the view to determining optimal container flows and YC requirements within a given planning time horizon. We designed a Branch and Cut (B&C) algorithm to solve the problem to optimality which was computationally evaluated. A novel heuristic approach based on the IP formulation was developed and implemented in C++. Detailed computational results are reported for both the exact and heuristic algorithms using a large number of randomly generated test problems. A practical application of the proposed model in the context of a real case-study is also presented. Finally, a simulation model of container terminal operations based on discrete-event simulation has been developed and implemented with the view of validating the above optimisation model and using it as a test bed for evaluating different operational scenarios

Control of multiclass queueing systems with abandonments and adversarial customers

This thesis considers the defensive surveillance of multiple public areas which are the open, exposed targets of adversarial attacks. We address the operational problem of identifying a real time decision-making rule for a security team in order to minimise the damage an adversary can inflict within the public areas. We model the surveillance scenario as a multiclass queueing system with customer abandonments, wherein the operational problem translates into developing service policies for a server in order to minimise the expected damage an adversarial customer can inflict on the system. We consider three different surveillance scenarios which may occur in realworld security operations. In each scenario it is only possible to calculate optimal policies in small systems or in special cases, hence we focus on developing heuristic policies which can be computed and demonstrate their effectiveness in numerical experiments. In the random adversary scenario, the adversary attacks the system according to a probability distribution known to the server. This problem is a special case of a more general stochastic scheduling problem. We develop new results which complement the existing literature based on priority policies and an effective approximate policy improvement algorithm. We also consider the scenario of a strategic adversary who chooses where to attack. We model the interaction of the server and adversary as a two-person zero-sum game. We develop an effective heuristic based on an iterative algorithm which populates a small set of service policies to be randomised over. Finally, we consider the scenario of a strategic adversary who chooses both where and when to attack and formulate it as a robust optimisation problem. In this case, we demonstrate the optimality of the last-come first-served policy in single queue systems. In systems with multiple queues, we develop effective heuristic policies based on the last-come first-served policy which incorporates randomisation both within service policies and across service policies

Queueing network models of zoned RAID system performance

RAID systems are widely deployed, both as standalone storage solutions and as the building blocks of modern virtualised storage platforms. An accurate model of RAID system performance is therefore critical towards fulfilling quality of service constraints for fast, reliable storage. This thesis presents techniques and tools that model response times in zoned RAID systems. The inputs to this analysis are a specified I/O request arrival rate, an I/O request access profile, a given RAID configuration and physical disk parameters. The primary output of this analysis is an approximation to the cumulative distribution function of I/O request response time. From this, it is straightforward to calculate response time quantiles, as well as the mean, variance and higher moments of I/O request response time. The model supports RAID levels 0, 01, 10 and 5 and a variety of workload types. Our RAID model is developed in a bottom-up hierarchical fashion. We begin by modelling each zoned disk drive in the array as a single M/G/1 queue. The service time is modelled as the sum of the random variables of seek time, rotational latency and data transfer time. In doing so, we take into account the properties of zoned disks. We then abstract a RAID system as a fork-join queueing network. This comprises several queues, each of which represents one disk drive in the array. We tailor our basic fork-join approximation to account for the I/O request patterns associated with particular request types and request sizes under different RAID levels. We extend the RAID and disk models to support bulk arrivals, requests of different sizes and scheduling algorithms that reorder queueing requests to minimise disk head positioning time. Finally, we develop a corresponding simulation to improve and validate the model. To test the accuracy of all our models, we validate them against disk drive and RAID device measurements throughout