Real time systems have been a major area of study for many years. Advancements in electronics, computers, information technology and digital networks are fueling major changes in the area of real time systems. In this thesis, we look at some of the most commonly modeled real time task systems, such as the periodic task model, including more complex task models such as the sporadic task systems. Primary focus of researchers in these fields include how to guarantee hard real time requirement of any task specification, with the minimal utilization of available hardware resources. Advancement in technology has brought multi-cored architectures with shared memory and massively parallel computing devices within the reach of ordinary computer users. Hence, it makes sense to study existing and newer task models on a wide variety of hardware platforms. Periodic task model and systems with such task models have been designed and well understood. Newer models such as the sporadic task models have been proposed to capture a more larger variety of real time systems being designed and used. We focus on designing more efficient scheduling algorithms for the sporadic LL task model, and propose simpler proofs to some of the algorithms existing in current literature. This thesis also focuses on scheduling sporadic task systems, under both multiprocessor full-migration and multiprocessor partitioned scheme. We also provide approximation algorithms to efficiently determine feasibility of such task systems.

Multiple-input, multiple-output (MIMO) techniques have been proposed to meet the needs for higher data rates and lower delays in future wireless communication systems. The downlink capacity of multiuser MIMO systems is achieved when the system transmits to several users simultaneously. Frequently, many more users request service than the transmitter can simultaneously support. Thus, the transmitter requires a scheduling algorithm for the users, which must balance the goals of increasing throughput, reducing multiuser interference, lowering delays, ensuring fairness and quality of service (QoS), etc. In this thesis, we investigate the application of genetic algorithms (GAs) to perform scheduling in multiuser MIMO systems. GAs are a fast, suboptimal, low-complexity method of solving optimization problems, such as the maximization of a scheduling metric, and can handle arbitrary functions and QoS constraints. We first examine a system that transmits using capacity-achieving dirty paper coding (DPC). Our proposed GA structure both selects users and determines their encoding order for DPC, which affects the rates they receive. Our GA can also schedule users independently on different carriers of a multi-carrier system. We demonstrate that the GA performance is close to that of an optimal exhaustive search, but at a greatly reduced complexity. We further show that the GA convergence time can be significantly reduced by tuning the values of its parameters. While DPC is capacity-achieving, it is also very complex. Thus, we also investigate GA scheduling with two linear precoding schemes, block diagonalization and successive zero-forcing. We compare the complexity and performance of the GA with "greedy" scheduling algorithms, and find the GA is more complex, but performs better at higher signal-to-noise ratios (SNRs) and smaller user pool sizes. Both algorithms are near-optimal, yet much less complex than an exhaustive search. We also propose hybrid greedy-genetic algorithms to gain benefits from both types of algorithms. Lastly, we propose an improved method of optimizing the transmit covariance matrices for successive zero-forcing. Our algorithm significantly improves upon the performance of the existing method at medium to high SNRs, and, unlike the existing method, can maximize a weighted sum rate, which is important for fairness and QoS considerations. / Communications

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A wireless sensor network (WSN) is a collection of sensor nodes distributed over a geographical region to obtain the environmental data. It can have different types of applications ranging from low data rate event driven and monitoring applications to high data rate real time industry and military applications. Energy efficiency and reliability are the two major design issues which should be handled efficiently at all the layers of communication protocol stack, due to resource constraint sensor nodes and erroneous nature of wireless channel respectively. Media access control (MAC) is the protocol which deals with the problem of packet collision due to simultaneous transmissions by more than one neighboring sensor nodes. Time Division Multiple Access based (TDMA-based) and contention-based are the two major types of MAC protocols used in WSNs. In general, the TDMA-based channel access mechanisms perform better than the contention-based channel access mechanisms, in terms of channel utilization, reliability and power consumption, specially for high data rate applications in wireless sensor networks (WSNs). TDMA-based channel access employs a predefined schedule so that the nodes can transmit at their allotted time slots. Based on the frequency of scheduling requirement, the existing distributed TDMA-scheduling techniques can be classified as either static or dynamic. The primary purpose of static TDMA-scheduling algorithms is to improve the channel utilization by generating a schedule of smaller length. But, they usually take longer time to generate such a schedule, and hence, are not suitable for WSNs, in which the network topology changes dynamically. On the other hand, dynamic TDMA-scheduling algorithms generate a schedule quickly, but they are not efficient in terms of generated schedule length. We suggest a new approach to TDMA-scheduling for WSNs, that can bridge the gap between these two extreme types of TDMA-scheduling techniques, by providing the flexibility to trade-off between the schedule length and the time required to generate the schedule, as per the requirements of the underlying applications and channel conditions. The suggested TDMA-scheduling works in two phases. In the first phase, we generate a valid TDMA schedule quickly, which need not have to be very efficient in terms of schedule length. In the second phase, we iteratively reduce the schedule length in a manner, such that the process of schedule length reduction can be terminated after the execution of an arbitrary number of iterations, and still be left with a valid schedule. This step provides the flexibility to trade-off the schedule length with the time required to generate the schedule. In the first phase of above TDMA-scheduling approach, we propose two randomized, distributed and parallel TDMA-scheduling algorithms viz., Distributed TDMA Slot Scheduling (DTSS) and Randomized and Distributed TDMA (RD-TDMA) scheduling algorithm. Both the algorithms are based on graph coloring approach, which generate a TDMA schedule quickly with a fixed schedule length ( Colouring), where is the maximum degree of any node in the graph to be colored. The two algorithms differ in the channel access mechanism used by them to transmit control messages, and in the generated schedule for different modes of communication, i.e., unicast, multicast and broadcast. The novelty of the proposed algorithms lies in the methods, by which an uncolored node detects that the slot picked by it is different from the slots picked by all the neighboring nodes, and the selection of probabilities with which the available slots can be picked up. Furthermore, to achieve faster convergence we introduce the idea of dynamic slot-probability update as per which the nodes update their slot-probability by considering the current slot-probability of their neighboring nodes. Under the second phase of the proposed TDMA-scheduling approach, we provide two randomized and distributed schedule compaction algorithms, viz., Distributed Schedule Compaction (DSC) and Distributed Schedule Length Reduction (DSLR) algorithm, as the mechanism to trade-off the scheduling time with the generated schedule length. These algorithms start with a valid TDMA schedule and progressively compress it in each round of execution. Additionally, Furthermore, the execution of these algorithms can be stopped after an arbitrary number of rounds as per the requirements of underlying applications. Even though TDMA-based MAC protocols avoid packet loss due to collision, due to erroneous nature of wireless medium, they alone are not sufficient to ensure the reliable transmission in WSNs. Automatic Repeat reQuest (ARQ) is the technique commonly used to provide error control for unicast data transmission. Unfortunately, ARQ mechanisms cannot be used for reliable multicast/broadcast transmission in WSNs. To solve this issue, we propose a virtual token-based channel access and feedback protocol (VTCAF) for link level reliable multicasting in single-hop wireless networks. The VTCAF protocol introduces a virtual (implicit) token passing mechanism based on carrier sensing to avoid the collision between feedback messages. The delay performance is improved in VTCAF protocol by reducing the number of feedback messages. Besides, the VTCAF protocol is parametric in nature and can easily trade-off reliability with the delay as per the requirements of the underlying applications. Finally, by integrating all the works, viz., TDMA-scheduling algorithms (DTSS/RD-TDMA), schedule compaction algorithms and link layer feedback mechanism for reliable multicast/ broadcast, we propose a TDMA-based energy aware and reliable MAC protocol, named TEA-MAC for multi-hop WSNs. Similar to VTCAF, TEA-MAC protocol uses the combination of ACK-based and NACK-based approaches to ensure reliable communication. But, instead of using virtual token-based channel access, it uses contention-based channel access for NACK transmission. All the algorithms and protocols proposed in this thesis are distributed, parallel and fault tolerant against packet losses to support scalability, faster execution and robustness respectively. The simulations have been performed using Castalia network simulator to evaluate the performance of proposed algorithms/protocols and also to compare their performance with the existing algorithms/protocols. We have also performed theoretical analysis of these algorithms/protocols to evaluate their performance. Additionally, we have shown the correctness of proposed algorithms/protocols by providing the necessary proofs, whenever it was required. The simulation results together with theoretical analysis show that, in addition to the advantage of trading the runtime with schedule length, the proposed TDMA scheduling approach achieves better runtime and schedule length performance than existing algorithms. Additionally, the TEA-MAC protocol is able to considerably improve the reliability and delay performance of multicast communication in WSNs.

A fundamental question in a sequential decision making setting under uncertainty is “how to allocate resources amongst competing entities so as to maximize the rewards accumulated in the long run?”. The resources allocated may be either abstract quantities such as time or concrete quantities such as manpower. The sequential decision making setting involves one or more agents interacting with an environment to procure rewards at every time instant and the goal is to find an optimal policy for choosing actions. Most of these problems involve multiple (infinite) stages and the objective function is usually a long-run performance objective. The problem is further complicated by the uncertainties in the sys-tem, for instance, the stochastic noise and partial observability in a single-agent setting or private information of the agents in a multi-agent setting. The dimensionality of the problem also plays an important role in the solution methodology adopted. Most of the real-world problems involve high-dimensional state and action spaces and an important design aspect of the solution is the choice of knowledge representation. The aim of this thesis is to answer important resource allocation related questions in different real-world application contexts and in the process contribute novel algorithms to the theory as well. The resource allocation algorithms considered include those from stochastic optimization, stochastic control and reinforcement learning. A number of new algorithms are developed as well. The application contexts selected encompass both single and multi-agent systems, abstract and concrete resources and contain high-dimensional state and control spaces. The empirical results from the various studies performed indicate that the algorithms presented here perform significantly better than those previously proposed in the literature. Further, the algorithms presented here are also shown to theoretically converge, hence guaranteeing optimal performance. We now briefly describe the various studies conducted here to investigate problems of resource allocation under uncertainties of different kinds: Vehicular Traffic Control The aim here is to optimize the ‘green time’ resource of the individual lanes in road networks that maximizes a certain long-term performance objective. We develop several reinforcement learning based algorithms for solving this problem. In the infinite horizon discounted Markov decision process setting, a Q-learning based traffic light control (TLC) algorithm that incorporates feature based representations and function approximation to handle large road networks is proposed, see Prashanth and Bhatnagar [2011b]. This TLC algorithm works with coarse information, obtained via graded thresholds, about the congestion level on the lanes of the road network. However, the graded threshold values used in the above Q-learning based TLC algorithm as well as several other graded threshold-based TLC algorithms that we propose, may not be optimal for all traffic conditions. We therefore also develop a new algorithm based on SPSA to tune the associated thresholds to the ‘optimal’ values (Prashanth and Bhatnagar [2012]). Our thresh-old tuning algorithm is online, incremental with proven convergence to the optimal values of thresholds. Further, we also study average cost traffic signal control and develop two novel reinforcement learning based TLC algorithms with function approximation (Prashanth and Bhatnagar [2011c]). Lastly, we also develop a feature adaptation method for ‘optimal’ feature selection (Bhatnagar et al. [2012a]). This algorithm adapts the features in a way as to converge to an optimal set of features, which can then be used in the algorithm. Service Systems The aim here is to optimize the ‘workforce’, the critical resource of any service system. However, adapting the staffing levels to the workloads in such systems is nontrivial as the queue stability and aggregate service level agreement (SLA) constraints have to be complied with. We formulate this problem as a constrained hidden Markov process with a (discrete) worker parameter and propose simultaneous perturbation based simulation optimization algorithms for this purpose. The algorithms include both first order as well as second order methods and incorporate SPSA based gradient estimates in the primal, with dual ascent for the Lagrange multipliers. All the algorithms that we propose are online, incremental and are easy to implement. Further, they involve a certain generalized smooth projection operator, which is essential to project the continuous-valued worker parameter updates obtained from the SASOC algorithms onto the discrete set. We validate our algorithms on five real-life service systems and compare their performance with a state-of-the-art optimization tool-kit OptQuest. Being ��times faster than OptQuest, our scheme is particularly suitable for adaptive labor staffing. Also, we observe that it guarantees convergence and finds better solutions than OptQuest in many cases. Wireless Sensor Networks The aim here is to allocate the ‘sleep time’ (resource) of the individual sensors in an intrusion detection application such that the energy consumption from the sensors is reduced, while keeping the tracking error to a minimum. We model this sleep–wake scheduling problem as a partially-observed Markov decision process (POMDP) and propose novel RL-based algorithms -with both long-run discounted and average cost objectives -for solving this problem. All our algorithms incorporate function approximation and feature-based representations to handle the curse of dimensionality. Further, the feature selection scheme used in each of the proposed algorithms intelligently manages the energy cost and tracking cost factors, which in turn, assists the search for the optimal sleeping policy. The results from the simulation experiments suggest that our proposed algorithms perform better than a recently proposed algorithm from Fuemmeler and Veeravalli [2008], Fuemmeler et al. [2011]. Mechanism Design The setting here is of multiple self-interested agents with limited capacities, attempting to maximize their individual utilities, which often comes at the expense of the group’s utility. The aim of the resource allocator here then is to efficiently allocate the resource (which is being contended for, by the agents) and also maximize the social welfare via the ‘right’ transfer of payments. In other words, the problem is to find an incentive compatible transfer scheme following a socially efficient allocation. We present two novel mechanisms with progressively realistic assumptions about agent types aimed at economic scenarios where agents have limited capacities. For the simplest case where agent types consist of a unit cost of production and a capacity that does not change with time, we provide an enhancement to the static mechanism of Dash et al. [2007] that effectively deters misreport of the capacity type element by an agent to receive an allocation beyond its capacity, which thereby damages other agents. Our model incorporates an agent’s preference to harm other agents through a additive factor in the utility function of an agent and the mechanism we propose achieves strategy proofness by means of a novel penalty scheme. Next, we consider a dynamic setting where agent types evolve and the individual agents here again have a preference to harm others via capacity misreports. We show via a counterexample that the dynamic pivot mechanism of Bergemann and Valimaki [2010] cannot be directly applied in our setting with capacity-limited alim¨agents. We propose an enhancement to the mechanism of Bergemann and V¨alim¨aki [2010] that ensures truth telling w.r.t. capacity type element through a variable penalty scheme (in the spirit of the static mechanism). We show that each of our mechanisms is ex-post incentive compatible, ex-post individually rational, and socially efficient

The central thesis of this dissertation is that by combining classical scheduling methodologies with those of inventory management and queueing theory we can better model, understand and solve complex real-world scheduling problems. In part II of this dissertation, we provide models of a realistic supply chain scheduling problem that capture both its combinatorial nature and its dependence on inventory availability. We present an extensive empirical evaluation of how well implementations of these models in commercially available software solve the problem. We are therefore able to address, within a specific problem, the need for scheduling to take into account related decision-making processes. In order to simultaneously deal with combinatorial and dynamic properties of real scheduling problems, in part III we propose to integrate queueing theory and deterministic scheduling. Firstly, by reviewing the queueing theory literature that deals with dynamic resource allocation and sequencing and outlining numerous future work directions, we build a strong foundation for the investigation of the integration of queueing theory and scheduling. Subsequently, we demonstrate that integration can take place on three levels: conceptual, theoretical and algorithmic. At the conceptual level, we combine concepts, ideas and problem settings from the two areas, showing that such combinations provide insights into the trade-off between long-run and short-run objectives. Next, we show that theoretical integration of queueing and scheduling can lead to long-run performance guarantees for scheduling algorithms that have previously been proved only for queueing policies. In particular, we are the first to prove, in two flow shop environments, the stability of a scheduling method that is based on the traditional scheduling literature and utilizes processing time information to make sequencing decisions. Finally, to address the algorithmic level of integration, we present, in an extensive future work chapter, one general approach for creating hybrid queueing/scheduling algorithms. To our knowledge, this dissertation is the first work that builds a framework for integrating queueing theory and scheduling. Motivated by characteristics of real problems, this dissertation takes a step toward extending scheduling research beyond traditional assumptions and addressing more realistic scheduling problems.

The central thesis of this dissertation is that by combining classical scheduling methodologies with those of inventory management and queueing theory we can better model, understand and solve complex real-world scheduling problems. In part II of this dissertation, we provide models of a realistic supply chain scheduling problem that capture both its combinatorial nature and its dependence on inventory availability. We present an extensive empirical evaluation of how well implementations of these models in commercially available software solve the problem. We are therefore able to address, within a specific problem, the need for scheduling to take into account related decision-making processes. In order to simultaneously deal with combinatorial and dynamic properties of real scheduling problems, in part III we propose to integrate queueing theory and deterministic scheduling. Firstly, by reviewing the queueing theory literature that deals with dynamic resource allocation and sequencing and outlining numerous future work directions, we build a strong foundation for the investigation of the integration of queueing theory and scheduling. Subsequently, we demonstrate that integration can take place on three levels: conceptual, theoretical and algorithmic. At the conceptual level, we combine concepts, ideas and problem settings from the two areas, showing that such combinations provide insights into the trade-off between long-run and short-run objectives. Next, we show that theoretical integration of queueing and scheduling can lead to long-run performance guarantees for scheduling algorithms that have previously been proved only for queueing policies. In particular, we are the first to prove, in two flow shop environments, the stability of a scheduling method that is based on the traditional scheduling literature and utilizes processing time information to make sequencing decisions. Finally, to address the algorithmic level of integration, we present, in an extensive future work chapter, one general approach for creating hybrid queueing/scheduling algorithms. To our knowledge, this dissertation is the first work that builds a framework for integrating queueing theory and scheduling. Motivated by characteristics of real problems, this dissertation takes a step toward extending scheduling research beyond traditional assumptions and addressing more realistic scheduling problems.

Multi functional health monitoring wearable devices are quite prominent these days. Usually these devices are battery-operated and consequently are limited by their battery life (from few hours to a few weeks depending on the application). Of late, it was realized that these devices, which are currently being operated at fixed voltage and frequency, are capable of operating at multiple voltages and frequencies. By switching these voltages and frequencies to lower values based upon power requirements, these devices can achieve tremendous benefits in the form of energy savings. Dynamic Voltage and Frequency Scaling (DVFS) techniques have proven to be handy in this situation for an efficient trade-off between energy and timely behavior. Within imec, wearable devices make use of the indigenously developed MUSEIC v2 (Multi Sensor Integrated circuit version 2.0). This system is optimized for efficient and accurate collection, processing, and transfer of data from multiple (health) sensors. MUSEIC v2 has limited means in controlling the voltage and frequency dynamically. In this thesis we explore how traditional DVFS techniques can be applied to the MUSEIC v2. Experiments were conducted to find out the optimum power modes to efficiently operate and also to scale up-down the supply voltage and frequency. Considering the overhead caused when switching voltage and frequency, transition analysis was also done. Real-time and non real-time benchmarks were implemented based on these techniques and their performance results were obtained and analyzed. In this process, several state of the art scheduling algorithms and scaling techniques were reviewed in identifying a suitable technique. Using our proposed scaling technique implementation, we have achieved 86.95% power reduction in average, in contrast to the conventional way of the MUSEIC v2 chip’s processor operating at a fixed voltage and frequency. Techniques that include light sleep and deep sleep mode were also studied and implemented, which tested the system’s capability in accommodating Dynamic Power Management (DPM) techniques that can achieve greater benefits. A novel approach for implementing the deep sleep mechanism was also proposed and found that it can obtain up to 71.54% power savings, when compared to a traditional way of executing deep sleep mode. / Nuförtiden så har multifunktionella bärbara hälsoenheter fått en betydande roll. Dessa enheter drivs vanligtvis av batterier och är därför begränsade av batteritiden (från ett par timmar till ett par veckor beroende på tillämpningen). På senaste tiden har det framkommit att dessa enheter som används vid en fast spänning och frekvens kan användas vid flera spänningar och frekvenser. Genom att byta till lägre spänning och frekvens på grund av effektbehov så kan enheterna få enorma fördelar när det kommer till energibesparing. Dynamisk skalning av spänning och frekvens-tekniker (såkallad Dynamic Voltage and Frequency Scaling, DVFS) har visat sig vara användbara i detta sammanhang för en effektiv avvägning mellan energi och beteende. Hos Imec så använder sig bärbara enheter av den internt utvecklade MUSEIC v2 (Multi Sensor Integrated circuit version 2.0). Systemet är optimerat för effektiv och korrekt insamling, bearbetning och överföring av data från flera (hälso) sensorer. MUSEIC v2 har begränsad möjlighet att styra spänningen och frekvensen dynamiskt. I detta examensarbete undersöker vi hur traditionella DVFS-tekniker kan appliceras på MUSEIC v2. Experiment utfördes för att ta reda på de optimala effektlägena och för att effektivt kunna styra och även skala upp matningsspänningen och frekvensen. Eftersom att ”overhead” skapades vid växling av spänning och frekvens gjordes också en övergångsanalys. Realtidsoch icke-realtidskalkyler genomfördes baserat på dessa tekniker och resultaten sammanställdes och analyserades. I denna process granskades flera toppmoderna schemaläggningsalgoritmer och skalningstekniker för att hitta en lämplig teknik. Genom att använda vår föreslagna skalningsteknikimplementering har vi uppnått 86,95% effektreduktion i jämförelse med det konventionella sättet att MUSEIC v2-chipets processor arbetar med en fast spänning och frekvens. Tekniker som inkluderar lätt sömn och djupt sömnläge studerades och implementerades, vilket testade systemets förmåga att tillgodose DPM-tekniker (Dynamic Power Management) som kan uppnå ännu större fördelar. En ny metod för att genomföra den djupa sömnmekanismen föreslogs också och enligt erhållna resultat så kan den ge upp till 71,54% lägre energiförbrukning jämfört med det traditionella sättet att implementera djupt sömnläge.