In recent years more and more real-time applications run on multiprocessor or distributed systems. In such systems, a task may execute sequentially on many different processors. Such a task can be viewed as a linear chain of subtasks, each of which represents a segment of the task that executes on one of those processors. The response time of the task is measured from the release of its first subtask to the completion of its last subtask and is called the end-to-end response time. A task is schedulable if its end-to-end response time is never greater than the specified end-to-end relative deadline. This thesis deals with the problem of scheduling periodic tasks to meet their end-to-end deadlines. Specifically, the thesis focuses on fixed-priority scheduling algorithms, where each subtask is assigned a fixed priority and is scheduled preemptively. According to this approach, three related problems need to be solved. Priority Assignment : How we assign the priorities to subtasks so that...

Scheduling precedence-constrained tasks in a distributed real-time system is an NP-hard problem. As a result, the task allocation and scheduling algorithms that use these heuristics do not scale when applied to large distributed systems. In this paper, we propose a novel approach that eliminates inter-task dependencies using shared buffers between dependent tasks. The system correctness, with respect to data-dependency, is ensured by having each dependent task poll the shared buffers at a fixed rate. Tasks can, therefore, be allocated and scheduled independently of their predecessors. To meet the timing constraints of the original dependent-task system, we have developed a method to iteratively derive the polling rates based on endto-end deadline constraints. The overheads associated with the shared buffers and the polling mechanism are minimized by clustering tasks according to their communication and timing constraints. Our simulation results with the task allocation based on a simple first-fit bin packing algorithm showed that the proposed approach scales almost linearly with the system size, and clustering tasks greatly reduces the polling overhead. 1

. Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the call-scheduling problem is studied for star and tree networks. Lower and upper bounds on the worst-case performance of List-Scheduling (LS) and variants of it are obtained for call-scheduling with arbitrary bandwidth requirements and either unit call durations or arbitrary call durations. LS does not require advance knowledge of call durations and, hence, is an on-line algorithm. It has performance ratio (competitive ratio) at most 5 in star networks. A variant of LS for calls with unit durations is shown to have performance ratio at most 2 2 3 . In tree networks with n nodes, a variant of LS for calls with unit durations has performance ratio at most 6, and a variant for calls with arbitrary d...

When a parallel computation is represented in a formalism that imposes series-parallel structure on its task graph, it becomes amenable to automated analysis and scheduling. Unfortunately, its execution time will usually also increase as precedence constraints are added to ensure series-parallel structure. Bounding the slowdown ratio would allow an informed tradeoff between the benefits of a restrictive formalism and its cost in loss of performance. This dissertation deals with series-parallelising task graphs by adding precedence constraints to a task graph, to make the resulting task graph series-parallel. The weak bounded slowdown conjecture for series-parallelising task graphs is introduced. This states that the slowdown is bounded if information about the workload can be used to guide the selection of which precedence constraints to add. A theory of best series-parallelisations is developed to investigate this conjecture. Partial evidence is presented that the weak slowdown bound is likely to be 4/3, and this bound is shown to be tight.

We consider a set of tasks of unit execution times and a bipartite precedence delays graph with a positive precedence delay d : an arc (i; j) of this graph means that j can be executed at least d time units after the completion time of i. The problem is to sequence the tasks in order to minimize the makespan. Firstly, we prove that the associated decision problem is NP-complete. Then, we provide a non trivial polynomial time algorithm if the degree of every tasks from one of the two sets is 2. Lastly, we give an approximation algorithm with ratio 3 2 . 1

If X 1 , X 2 , . . . , X n is a sequence of non-negative independent random variables with common distribution function F (t), we write X (n) for the maximum of the sequence and S n for its sum. The ratio variate R n = X (n) /S n is a quantity arising in the analysis of process speedup and the performance of scheduling. O'Brien (1980) showed that R n ® 0 almost surely Û EX 1 < as n ® . Since {R n } is a uniformly bounded sequence it follows that EX 1 < Þ ER n ® 0 as n ® . Here we show that, provided either that (i) EX 1 2 < or that (ii) 1 - F(t) is a regularly varying function with index r < -1, it follows that ER n = ES n EX (n) ###### # # 1 + o(1) # # (n ® ) . Since the asymptotics of EX (n) is often readily calculated, this provides a useful estimate for the most significant behavior of the ratio R n in expectation. We apply this result to multiprocessor scheduling policies and to the behavior of sample statistics. June 28, 1994 Department of Computer Science The Univer...

Polyhedral Combinatorics approaches have turned out to be successful computational tools in many hard Combinatorial Optimization problems. We present an approximation algorithm based on linear programming formulations with binary decision variables which are a kind of assignment variables for the classical deterministic scheduling problem of minimizing the makespan on identical machines. The problemisknowntobeNP-hard in the strong sense. The structure of the corresponding polytope is analyzed, and the strong cutting planes are identi ed. Computational results show that, in all tested cases, the problem can be solved exactly. Keywords: Optimization, Polyhedral Combinatorics, Scheduling.

Using a simple multiprocessor scheduling problem as a vehicle, we explore the behavior of tabu search algorithms using different tabu, local search and list management strategies. We found that random blocking of the tail of the tabu list always improved performance; but that the use of frequency-based penalties to discourage frequently selected moves did not. Hash coding without conflict resolution was an effective way to represent solutions on the tabu list. We also found that the most effective length of the tabu list depended on features of the algorithm being used, but not on the size and complexity of the problem being solved. The best combination of features included random blocking of the tabu list, tasks as tabus and a greedy local search. An algorithm using these features was found to outperform a recently published algorithm solving a similar problem.