No / Quality of Service (QoS) is of extreme importance in accommodating the increasingly diverse range of services and types of traffic in present day communication networks and delay is one of the most important QoS metrics. This paper presents a new approach for constraining queueing delay in a buffer to a specified level as the arrival rate changes with time. A discrete-time control algorithm is presented that operates on a buffer (queue) which incorporates a moveable threshold. An algorithm is developed that controls the delay by dynamically adjusting the threshold which, in turn, controls the arrival rate. The feasibility of the system is examined using both theoretical analysis and simulation.

No / Over the last few years, cloud computing has become quite popular. It offers Web-based companies the advantage of scalability. However, this scalability adds complexity which makes analysis and predictable performance difficult. There is a growing body of research on load balancing in cloud data centres which studies the problem from the perspective of the cloud provider. Nevertheless, the load balancing of scalable web servers deployed on the cloud has been subjected to less research. This paper introduces a simple queueing model to analyse the performance metrics of web server under varying traffic loads. This assists web server managers to manage their clusters and understand the trade-off between QoS and cost. In this proposed model two thresholds are used to control the scaling process. A discrete-event simulation (DES) is presented and validated via an analytical solution.

Developing equations to compute congestion measures for the general G/G/s/c queueing model and networks of such nodes has always been a challenge. One approach to analyzing such systems is to approximate the model-specified general input processes and distributions by processes and distributions from the more computationally friendly family of phase-type processes and distributions. We develop numerical approximation methods for analysis of general time-dependent queueing nodes by introducing new approximations for the time-dependent first two moments of the number-in-system and departure-count processes. / Ph. D.

Cell biology is a branch of science with a seemingly infinite abundance of interesting phenomena which are essential to our understanding of life and which may potentially drive the development of technology that improves our lives. Among the open ended questions within the field, an understanding of how gene networks are affected by limited cellular components is both broad and rich with interest. Common to all cellular systems are enzymes which perform many tasks within cells without which organisms could not remain healthy. Here are presented several explorations of enzymatic processing as well as a tool constructed for this purpose. More specifically, these works consider the effect of coupling of gene networks via competition for enzymes found within the cell. It is shown that a limitation on the number of available enzymes permits the formation of bottlenecks which drastically affect molecular dynamics within cells. These effects potentially afford cell behaviors that in part explain the impressive robustness of life to constantly fluctuating environments. / Ph. D.

This paper presents a new analytical framework for the congestion control of Internet traffic using a queue threshold scheme. This framework includes two discrete-time analytical models for the performance evaluation of a threshold based congestion control mechanism and compares performance measurements through typical numerical results. To satisfy the low delay along with high throughput, model-I incorporates one threshold to make the arrival process step reduce from arrival rate ¿1 directly to ¿2 once the number of packets in the system has reached the threshold value L1. The source operates normally, otherwise. Model-II incorporates two thresholds to make the arrival rate linearly reduce from ¿1 to ¿2 with system contents when the number of packets in the system is between two thresholds L1 and L2. The source operates normally with arrival rate ¿1 before threshold L1, and with arrival rate ¿2 after the threshold L2. In both performance models, the mean packet delay W, probability of packet loss PL and throughput S have been found as functions of the thresholds and maximum drop probability. The performance comparison results for the two models have also been made through typical numerical results. The results clearly demonstrate how different load settings can provide different tradeoffs between throughput, loss probability and delay to suit different service requirements.

Time-dependent queueing models are important since most of real-life problems are time-dependent. We develop a numerical approximation algorithm for the mean, variance and higher-order moments of the number of entities in the system at time t for the Ph(t)/Ph(t)/s/c queueing model. This model can be thought as a reparameterization to the G(t)/GI(t)/s. Our approach is to partition the state space into known and identifiable structures, such as the M(t)/M(t)/s/c or M(t)/M(t)/1 queueing models. We then use the Polya-Eggenberger distribution to approximate certain unknown probabilities via a two-moment matching algorithm. We describe the necessary steps to validate the approximation and measure the accuracy of the model. / Master of Science

A deterministic change to a time-varying queueing model is described as either changing the number of entities, the queue capacity, or the number of servers in the system at selected times. We use a surrogate distribution for N(t), the number of entities in the system at time t, to approximate deterministic changes to the Ph(t)/Ph(t)/1/c and the Ph(t)/M(t)/s/c queueing models. We develop a solution technique to minimize the number of state probabilities to be approximated. / Master of Science

The Internet has been more and more intensively used in recent years. Although network infrastructure has been regularly upgraded, and the ability to manage heavy traffic greatly increased, especially on the core networks, congestion never ceases to appear, as the amount of traffic that flow on the Internet seems to be increasing at an even faster rate. Thus, congestion control mechanisms play a vital role in the functioning of the Internet. Active Queue Management (AQM) is a popular type of congestion control mechanism that is implemented on gateways (most notably routers), which can predict and avoid the congestion before it happens. When properly configured, AQMs can effectively reduce the congestion, and alleviate some of the problems such as global synchronisation and unfairness to bursty traffic. However, there are still many problems regarding AQMs. Most of the AQM schemes are quite sensitive to their parameters setting, and these parameters may be heavily dependent on the network traffic profile, which the administrator may not have intensive knowledge of, and is likely to change over time. When poorly configured, many AQMs perform no better than the basic drop-tail queue. There is currently no effective method to compare the performance of these AQM algorithms, caused by the parameter configuration problem. In this research, the aim is to propose a new analytical model, which mainly uses discrete-time queueing theory. A novel transient modification to the conventional equilibrium-based method is proposed, and it is utilised to further develop a dynamic interactive model of responsive traffic and bottleneck queues. Using step-by-step analysis, it represents the bursty traffic and oscillating queue length behaviour in practical network more accurately. It also provides an effective way of predicting the behaviour of a TCP-AQM system, allowing easier parameter optimisation for AQM schemes. Numerical solution using MATLAB and software simulation using NS-2 are used to extensively validate the proposed models, theories and conclusions.

This thesis provides a discrete-event simulation framework that can be used to analyze  and  dimension  computing  systems.  The  simulation  framework  can define  and  parametrize  the  flexible  queueing  system.  We  use  the  simulation framework to explore the data collected from the real-world system. We analyze the metrics, including waiting time and server utilization of single-server and multi-server  queueing  systems.  In  particular,  we  study  the  impact  of  the number of servers on waiting time and server utilization. The experiments show it  is  possible  to  increase  server  utilization  and  decrease  the  server  number without  significantly  increasing  waiting  time,  and  flexible  architectures  canlead to significant gains. / Detta  examensarbete  tillhandahåller  ett  ramverk  som  kan  användas  för  att analysera och dimensionera dator-system. Simuleringsramverket kan definera och parameterisera ett flexibelt kösystem baserat på data från ett system i drift. Vi använder simuleringsramverket för att undersöka datat insamlat från skarpa system.  Vi  analyserar  prestandatal,  såsom  väntetid  och  utnyttjandegrad  för system  med  en  och  flera  betjänare.  Framför  allt  undersöker  vi  hur  antalet betjänare  påverkar  väntetid  och  utnyttjandegrad.   Försöken  visar  att  det  är möjligt  att  öka  uttnyttjandegraden  och  minska  antalet  betjänare  utan  att märkbart öka väntetiden, och att en flexibel arkitektur kan leda till märkbaraförbättringar. / <p>Industrial Advisors: Olga Grinchtein and Johan Karlsson </p>

"A distributed queueing Medium Access Control (MAC) protocol is used in Distributed Queue Dual Bus (DQDB) networks. A modified version of the MAC protocol was proposed by R.R. Pillai and U. Mukherji in an attempt to overcome some of the shortcomings of the DQDB MAC protocol. They analyzed the performance of the system for Bernoulli arrivals and for large propagation delays between the nodes. We extend the performance analysis of the modified MAC protocol for a DQDB type of Network. The parameter of interest to us is the bus access delay. This has two components, viz., the request bus access delay and the data bu6 access delay. We use the model at the request point at node and present methods to evaluate the delay experienced in such a model. The model is an n-priority ./D/l queue with D vacations (non-preemptive priority) where n is the number of nodes sending requests on the request bus for transmission on the data bus. The methods presented help to evaluate the request bus access delay when the arrivals at each node are Markovian Arrival Processes (MAPs). The algorithms for evaluating the mean request bus access delay are based on matrix geometric techniques. Thus, one can use the algorithms developed in the literature to solve for the finite buffers case too. This model, for the request bus access delay, holds irrespective of the propagation delay between the nodes. We also evaluate the inter-departure time of class 1 customers and virtual customers in a 2-priority M/G/l system with G vacations (non-preemptive priority). In the case of Poisson arrivals at all the nodes, we would have a 2-priority M/D/l system with D vacations (non-preemptive priority). We thus evaluate the inter-arrival time of the free slots on the data bus as seen by Node 2. Note that this is independent of the number of active nodes in the network We then develop methods to evaluate the mean data bus access delay experienced by the customers at Node 2 in a three-node network with 2 nodes communicating with the third when the propagation delay between the nodes is large. We consider the case of finite Local Queue buffers at the two nodes. Using this assumption we arrive at process of arrivals to the Combined Queue and the process of free slots on the data bus to be Markov Modulated Bernoulli processes. The model at the combined queue at Node 2 then has a Quasi Birth-Death evolution. Thus, this system is solved by using the Ramaswami-Latouche algorithm. The stationary probabilities are then used to evaluate the mean data bus access delay experienced at Node 2. The finite buffer case of this system can be solved by G.Wi Stewart's algorithm. The method in modelling the system and the results are presented in detail for Poisson arrivals. The extension of this to more complex processes is also explained. We encounter in the analysis an explosion of the state-space of the system. We try to counter this by considering approximations to the process of free slots on the data bus. The approximations considered are on the basis of what are known as Idealized Aggregates. The performance of the approximation is also detailed. It works very well under low and moderate load but underestimates the mean delay under heavy load. Thereafter, we discuss the performance of the system with reference to the mean of the access delay and the standard deviation of the access delay under varying traffic at the two nodes. For this part we use simulation results to discuss the performance. The comparison between the performance measures at both the nodes is also done. Then we develop methods/techniques to understand the performance of the system when we have finite propagation delays between the nodes. We concentrate on the 3-node problem and calculate performance bounds based on linear programs. This is illustrated in detail for Bernoulli arrivals for the case of 1 slot propagation delay between the nodes as well as for the case of 2 slots propagation delay. The performance of the bounds obtained is also detailed. The presence of an idling system at the combined queue of Node 2 makes the bounds somewhat loose. Finally, we discuss the performance of the system with reference to the mean access delay and the standard deviation of the access delay under varying load on the system. Again, we rely on simulation studies. Finally, we study the performance of the system as a multiplexer. For this, we re­strict the traffic to Markov Modulated Processes (or those which would satisfy the Gartner-Ellis Theorem requirements). The traffic is characterized by what are known as Envelope Processes - Lower and Upper. The class of processes which satisfy the conditions of the Gartner-Ellis theorem come under the category where both the Envelope Processes exist and the Minimum Envelope Rate and the Maximum Lower Envelope Rate are the same. We use the system evolution equations at the combined queue at any node to develop re­lations between the various input and output processes. First, this is done for a. system of this kind, in isolation. Then, we consider this system as a part of the modified protocol and present relations, among the various input and output processes, which are specific to the modified protocol. The possible use of all of the above to do Admission Control at the entry point to the Asynchronous Transfer Mode (ATM) network is also presented.