Battery-powered portable embedded systems have been widely used in many applications. These embedded systems have to concurrently perform a multitude of complex tasks under stringent time constraints. As these systems become more complex and incorporate more functionality, they became more power-hungry. Thus, reducing power consumption and extending battery lifespan while guaranteeing the timing constraints has became a critical aspect in designing such systems. This gives rise to three aspects of research: (i) Guaranteeing the execution of the hard real-time tasks by their deadlines, (ii) Determining the minimum voltage under which each task can be executed, and (iii) Techniques to take advantage of run-time variations in the execution times of tasks. In this research, we present techniques that address the above aspects in single and multi processor embedded systems. We study the performance of the proposed techniques on various benchmarks in terms of energy savings.

Battery-powered portable embedded systems have been widely used in many applications. These embedded systems have to concurrently perform a multitude of complex tasks under stringent time constraints. As these systems become more complex and incorporate more functionality, they became more power-hungry. Thus, reducing power consumption and extending battery lifespan while guaranteeing the timing constraints has became a critical aspect in designing such systems. This gives rise to three aspects of research: (i) Guaranteeing the execution of the hard real-time tasks by their deadlines, (ii) Determining the minimum voltage under which each task can be executed, and (iii) Techniques to take advantage of run-time variations in the execution times of tasks. In this research, we present techniques that address the above aspects in single and multi processor embedded systems. We study the performance of the proposed techniques on various benchmarks in terms of energy savings.

This work presents a novel slack management technique, the Service Rate Based Slack Distribution Technique, for dynamic real-time distributed embedded systems targeting the reduction and management of energy consumption. Energy minimization is critical for devices such as laptop computers, PCS telephones, PDAs and other mobile and embedded computing systems simply because it leads to extended battery lifetime. Such systems being power hungry rely greatly upon the system design and algorithms for processing, slack and power management. This work presents an effcient dynamic slack management scheme for an energy aware design of such systems. The proposed Service Rate Based Slack Distribution Technique has been considered with two static(FCFS, WRR) and two dynamic(EDF, RBS) scheduling schemes used most commonly in distributed systems. A fault tolerance mechanism has also been incorporated into the proposed technique inorder to use the available dynamic slack to maintain checkpoints and provide for rollbacks on faults. Results show that in comparion to contemporary techniques, the proposed Service Rate Based Slack Distribution Technique provides for about 29% more perfor-mance/overhead savings when validated with real world and random benchmarks.

This work presents a novel slack management technique, the Service Rate Based Slack Distribution Technique, for dynamic real-time distributed embedded systems targeting the reduction and management of energy consumption. Energy minimization is critical for devices such as laptop computers, PCS telephones, PDAs and other mobile and embedded computing systems simply because it leads to extended battery lifetime. Such systems being power hungry rely greatly upon the system design and algorithms for processing, slack and power management. This work presents an effcient dynamic slack management scheme for an energy aware design of such systems. The proposed Service Rate Based Slack Distribution Technique has been considered with two static(FCFS, WRR) and two dynamic(EDF, RBS) scheduling schemes used most commonly in distributed systems. A fault tolerance mechanism has also been incorporated into the proposed technique inorder to use the available dynamic slack to maintain checkpoints and provide for rollbacks on faults. Results show that in comparion to contemporary techniques, the proposed Service Rate Based Slack Distribution Technique provides for about 29% more perfor-mance/overhead savings when validated with real world and random benchmarks.

In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random variables. We derive a diffusion approximation using a novel method. The diffusion has a random drift, and hence depending on the realisations of service rates, the system can be in Quality Driven (QD), Efficiency Driven (ED) or Quality-Efficiency-Driven (QED) regime. When the system is under QD or QED regime, the abandonments are negligible in the fluid limit, but when it is under ED regime, the probability of abandonment will converge to a non-zero value. We then analyse the optimal staffing levels to balance holding costs with staffing costs combining these three regimes. We also analyse how the variance of service rates influence abandonment rate. Next, we focus on the state space collapse (SSC) phenomenon. We prove that under some assumptions, the system process will collapse to a lower dimensional process without losing essential information. We first formulate a general method to prove SSC results inside pools for heavy traffic systems using the hydrodynamic limit idea. Then we work on the SSC in multi-class queueing networks under the Halfin-Whitt heavy traffic when service rates are i.i.d. random variables within pools. For such systems, exact analysis provides limited insight on the general properties. Alternatively, asymptotic analysis by diffusion approximation proves to be effective. Further, limit theorems, which state the diffusively scaled system process weakly converges to a diffusion process, are usually the central part in such asymptotic analysis. The SSC result is key to proving such a limit. We conclude by giving examples on how SSC is applied to the analysis of systems.

The determination of the right number of servers in a multi-server queueing system is one of the most important problems in applied queueing theory. The problem becomes more complex in a system that consists of both cross-trained and specialized servers. Such queueing systems are readily found in the call centres (also called contact centres) of financial institutions, telemarketing companies and other organizations that provide services to customers in multiple languages. They are also found in computer network systems where some servers are dedicated and others are flexible enough to handle various clients' requests. Over-staffing of these systems causes increased labour costs for the underutilized pool of agents on duty, while under-staffing results in reduced revenue from lost customers and an increase in queue times. The efficient design and analysis of these systems helps management in making better staffing decisions. This thesis aims to develop models for establishing agent staffing levels in organizations with cross-trained and specialized staff with a view to minimizing cost and maintaining a desirable customer satisfaction. The work investigates the effect of various traffic loads on the number of agents required and the cost. It also considers how using specialized agents, flexible agents and a combination of both categories of agents affects the system. It uses a contact centre that has agents with monolingual, bilingual and trilingual (English, French and Spanish) capabilities to do the study.

The determination of the right number of servers in a multi-server queueing system is one of the most important problems in applied queueing theory. The problem becomes more complex in a system that consists of both cross-trained and specialized servers. Such queueing systems are readily found in the call centres (also called contact centres) of financial institutions, telemarketing companies and other organizations that provide services to customers in multiple languages. They are also found in computer network systems where some servers are dedicated and others are flexible enough to handle various clients' requests. Over-staffing of these systems causes increased labour costs for the underutilized pool of agents on duty, while under-staffing results in reduced revenue from lost customers and an increase in queue times. The efficient design and analysis of these systems helps management in making better staffing decisions. This thesis aims to develop models for establishing agent staffing levels in organizations with cross-trained and specialized staff with a view to minimizing cost and maintaining a desirable customer satisfaction. The work investigates the effect of various traffic loads on the number of agents required and the cost. It also considers how using specialized agents, flexible agents and a combination of both categories of agents affects the system. It uses a contact centre that has agents with monolingual, bilingual and trilingual (English, French and Spanish) capabilities to do the study.

The master’s thesis solves models of queueing systems, which use the property of Markov chains. The queueing system is a system, where the objects enter into this system in random moments and require the service. This thesis solves specifically such models of queueing systems, in which the intervals between the objects incomings and service time have exponential distribution. In the theoretical part of the master’s thesis I deal with the topics stochastic process, queueing theory, classification of models and description of the models having Markovian property. In the practical part I describe realization and function of the program, which solves simulation of chosen model M/M/m. At the end I compare results which were calculated in analytic way and by simulation of the model M/M/m.