Thomas G. Robertazzi

Divisible Load Theory: A New Paradigm for Load Scheduling in Distributed Systems

Divisible load theory is a methodology involving the linear and continuous modeling of partitionable computation and communication loads for parallel processing. It adequately represents an important class of problems with applications in parallel and distributed system scheduling, various types of data processing, scientific and engineering computation, and sensor networks. Solutions are surprisingly tractable. Research in this area over the past decade is described.

Computer Networks and Systems: Queueing Theory and Performance Evaluation

From the Publisher: This text, intended for a first course in performance evaluation, is a self-contained treatment covering all aspects of queuing theory. It starts by introducing readers to the terminology and usefulness of queuing theory and continues by considering Markovian queues in equilibrium, Littles law, reversibility, transient analysis, and computation, and the M/G/1 queuing system. A subsequent chapter covers networks of queues including the presentation of a recent and clear topological explanation for the existence of the product form solution. The final chapters explain techniques for numerical solutions, such as the convolution algorithm and mean-value analysis; discuss the PANACEA technique, discrete time queuing systems and simulation; and describe the new area of stochastic Petri networks. Case studies of distributed queuing networks arising in industrial applications are included. An appendix reviews probability theory. The third edition includes a new chapter on self-similar traffic, many new problems, and solutions for many exercises.

Distributed computation with communication delay (distributed intelligent sensor networks)

A linear network of communicating processors is examined. The objective is to solve a computational problem in a minimal amount of time. The processors in the networks may be equipped either with or without front-end processors for communication off-loading. The cases of equal division of processing load and optimal division of processing load are discussed for both the network with front-end processors and the network without front end processors. An example of the inclusion of solution time, the time taken for processors to report the solution back to the problem originator, is also presented. >

Closed form solutions for bus and tree networks of processors load sharing a divisible job

Optimal load allocation for load sharing a divisi ble job over processors interconnected in either a bus or a tree network is considered. The processors are either equipped with front-end processors or not so equipped. Closed form solutions for the minimum fin ish time and the optimal data allocation for each pro cessor are obtained. The performance of large sym metric tree networks is examined by aggregating the component links and processors into a single equiv alent processor. This allows an easy examination of large tree networks. In addition it becomes possible to find a closed form solution for the optimal amount of data that is to be assigned to each processor in the tree network in order to achieve the minimum finish time.

Markovian Petri Nets protocols with product form solution

Abstract A class of Markovian Petri Net models whose equilibrium state probabilities satisfy detailed (local) balance equations is presented. Examples of their applicability include a bus oriented multiprocessor model, a version of the classical dining philosophers problem and an alternating bit protocol model. The natural topological space for embedding the state transition lattices for this class of MPNs is shown to be a multidimensional toroidal manifold.

Bus-oriented load sharing for a network of sensor driven processors

A load-sharing problem involving the optimal allocation of measurement data among n sensor-driven processors interconnected through a bus-type communication medium is considered for three distinct architectural configurations. It is found that a minimal-time solution can be achieved if the computations by the processors end simultaneously. Simple recursions for the determination of the optimal allocation of load are presented. It is shown that for this problem a small number of processors can be almost as effective as a larger number. >

Processor equivalence for daisy chain load sharing processors

A linear daisy chain of processors in which processor load is divisible and shared among the processors is examined. It is shown that two or more processors can be collapsed into a single equivalent processor. This equivalence allows a characterization of the nature of the minimal time solution, a simple method to determine when to distribute load for linear daisy chain networks of processors without front end communication subprocessors and closed form expressions for the equivalent processing speed of infinitely large daisy chains of processors. >

Wireless sensor networks: scheduling for measurement and data reporting

An optimal load allocation approach is presented for measurement and data reporting in wireless sensor networks with a single level tree network topology. The measurement problem investigated involves a measurement space, part of which can be sampled by each sensor. We seek to optimally assign sensors part of the measurement space to minimize reporting time and energy usage. Three representative measurement and reporting strategies are studied. This work is novel as it considers, for the first time, the measurement capacity of processors and assumes negligible computation time which is radically different from the traditional divisible load scheduling research to date. Aerospace applications include satellite remote sensing and monitoring and sensor networks deployed and monitored from the air.

Optimal divisible job load sharing for bus networks

Optimal load allocation for load sharing a divisible job over N processors interconnected in bus-oriented network is considered. The processors are equipped with front-end processors. It is analytically proved, for the first time, that a minimal solution time is achieved when the computation by each processor finishes at the same time. Closed form solutions for the minimum finish time and the optimal data allocation for each processor are also obtained.

Layer net: a new self-organizing network protocol

A protocol is proposed for the generation and operation of a self-organizing multihop radio network, which is capable of creating its own topology and transmission schedules dynamically and in a distributed manner. The protocol commences operation in a random-access mode of operation and then gradually switches over to a synchronous schedules mode of operation. The protocol was simulated up to the end of the scheduling phase. This included the generation of node positions, tree formation, addition of links and the scheduling of these links. The percentage increase in average hop distance between nodes in the generated network over the fully connected network (the network with all possible links between physical neighbors) was found to vary between 10% to 15%. Empirically, it appears that a schedule length that is twice the maximum degree is sufficient to allow the distributed generation of a conflict-free schedule.<<ETX>>