In this paper, analytical models for a multiprocessor executing a stream consisting of K classes of fork-join jobs are developed.Here, a fork-join job consists of a random number of tasks that can beexecuted independently ofeach other.Several priority policies are analyzed:(a) a strict nonpreemptive head of the line policy (b) a preemptive policy that allows preemptions at the job level, (c) a preemptive policy that allows preemptions at the task level, and (d) a policy in which the priority is a nondecreasing function of the number of tasks in the queue with preemptions at the job level.Using these models, the mean job response time for the different classes under the different policies is compared.These policies are compared to a system in which processors are partitioned so that classes are allocated only to certain processor groups.It is shown that, for the system considered, the task preemption policy has a uniformly better mean class response time and thus is preferable to a system with partitioned processors.

In shared-memory multiprocessor systems it may be more efficient to schedule a task on one processor than on mother. Due to the inevitability of idle processors in these environments, there exists an important tradeoff between keeping the workload balanced and scheduling tasks where they run most efficiently. The purpose of an adaptive task migration policy is to determine the appropriate balance between the extremes of this load sharing tradeoff.We make the observation that there are considerable differences between this load sharing problem in distributed and shared-memory multiprocessor systems, and we formulate a queueing theoretic model of task migration to study the problem. A detailed mathematical analysis of the model is developed, which includes the effects of increased contention for system resources induced by the task migration policy. Our objective is to provide a better understanding of task migration in shared-memory multiprocessor environments. In particular, we illustrate the potential for significant improvements in system performance, and we show that even when migration costs are large it may still be beneficial to migrate waiting tasks to idle processors. We further demonstrate the potential for unstable behavior under migratory scheduling policies, and we provide optimal policy thresholds that yield the best performance and avoid this form of processor thrashing.

In this paper we analyze a model of a parallel processing system. In our model there is a single queue which is K ≥ 1 identical processors. Jobs are assumed to consist of a sequence of barrier synchronizations where, at each step, the number of tasks that must be synchronized is random with a known distribution. An exact analysis of the model is derived. The model leads to a rich set of results characterizing the performance of parallel processing systems. We show that the number of jobs concurrently in execution, as well as the number of synchronization variables, grows linearly with the load of the system and strongly depends on the average number of parallel tasks found in the workload. Properties of expected response time or such systems are extensively analyzed and, in particular, we report on some non-obvious response time behavior that arises as a function of the variance of parallelism found in the workload. Based on exact response time analysis, we propose a simple calculation that can be used as a rule of thumb to predict speedups. This can be viewed as a generalization of Amdahl's law that includes queueing effects. This generalization is reformulated when precise workloads cannot be characterized, but rather when only the fraction or sequential work and the average number of parallel tasks arc assumed to be known.

In this paper we derive an approximation for the mean response time of a multiple queue system in which shortest queue routing is used. We assume there are Κ identical queues with infinite capacity and service times that are exponentially distributed. Arrivals of jobs to this system are Poisson and are routed to a queue of minimal length. We develop an approximation which is based on both theoretical and experimental considerations and, for Κ ≤ 8, has an relative error of less than one half of one percent when compared to simulation. For Κ = 16, the relative error is still acceptable, being less than 2 percent. An application to a model of parallel processing and a comparison of static and dynamic load balancing schemes are presented.

A bulk arrival M/sup x//M/c queuing system is used to model a centralized parallel processing system with job splitting. In such a system, jobs wait in a central queue, which is accessible by all the processors, and are split into independent tasks that can be executed on separate processors. The job response-time consists of three components: queuing delay, service time, and synchronization delay. An expression for the mean job response-time is obtained for this centralized parallel-processing system. Centralized and distributed parallel-processing systems (with and without job-splitting) are considered and their performances compared. Furthermore, the effects of parallelism and overheads due to job-splitting are investigated.>

A centralized parallel processing system with job splitting is considered. In such a system, jobs wait in a central queue, which is accessible by all the processors, and are split into independent tasks that can be executed on separate processors. This parallel processing system is modeled as a bulk arrival MX/M/c queueing system where customers and bulks correspond to tasks and jobs, respectively. Such a system has been studied in [1, 3] and an expression for the mean response time of a random customer is obtained. However, since we are interested in the time that a job spends in the system, including synchronization delay, we must evaluate the bulk response time rather than simply the customer response time. The job response time is the sum of the job waiting time and the job service time. By analyzing the bulk queueing system we obtain an expression for the mean job waiting time. The mean job service time is given by a set of recurrence equations.

In this paper catastrophic behavior found in computer systems is investigated. Deterministic Catastrophe theory is introduced first. Then it is shown how the theory can be applied in a stochastic framework, which is useful for understanding computer system performance models. Computer system models that exhibit stochastic cusp catastrophe behavior are then analyzed. These models include slotted ALOHA, multiprogramming in computer systems, and buffer flow control in computer networks.

In this paper, we define a two-parameter family of protocols designed for multihop packet radio networks. We call these protocols rude-CSMA because under certain circumstances, maximum throughput is obtained when nodes, even after sensing a busy channel, transmit packets anyway with a nonzero rate. The performance of these protocols is analyzed for various special and random topologies.

In this paper we define a broadcast channel access protocol called spatial TDMA, which is designed specifically to operate in a multihop packet radio environment where the location of the nodes of the network is assumed to be fixed. The defined protocol assigns transmission rights to nodes in the network in a local TDMA fashion and is collisionfree. Methods for determining slot allocations are developed, and an approximate solution is given for determining the assignment of capacities for the links of the network that minimizes the average delay of messages in the system.

In this paper we determine throughput equations for a packet radio network where terminals are randomly distributed on the plane, are able to capture transmitted signals, and use slotted ALOHA to access the channel. We find that the throughput of the network is a strictly increasing function of the receiver's ability to capture signals, and depends on the transmission range of the terminals and their probability of transmitting packets. Under ideal circumstances, we show the expected fraction of terminals in the network that are engaged in successful traffic in any slot does not exceed 21 percent.