Igal Adiri

Single machine flow-time scheduling with a single breakdown

SummaryWe consider the problem of scheduling tasks on a single machine to minimize the flowtime. The machine is subject to breakdowns during the processing of the tasks. The breakdowns occur at a random times and the machine is unavailable until it is repaired. The times for repair are random and independent of each other and of the breakdown process. A task that is preempted due to a breakdown must be restarted and otherwise preemptions are not allowed. We show in the case of a single breakdown that if the distribution function of the time to breakdown is concave then Shortest Processing Time (SPT) first scheduling stochastically minimizes the flowtime. For the case of multiple breakdowns we show that SPT minimizes the expected flowtime when the times to breakdown are exponentially distributed. If the time for a single breakdown is known before scheduling begins, and the processing times of the tasks are also known, then we show that the problem of deciding whether there is a schedule with flowtime less than or equal to a given value is NP-complete. Finally, we bound the performance of SPT scheduling in the deterministic case when there is a single breakdown.

Openshop and flowshop scheduling to minimize sum of completion times

Abstract This paper deals with efficiently solvable special cases of openshop and permutation-flowshop scheduling where the objective function is minimum sum of completion times. Two O(mn) algorithms for openshop scheduling where all operations have equal processing times, are presented. The first constructs a no-wait schedule and the second a schedule where both criteria (sum of completion times and schedule length) take on their minimal values. For permutation-flowshop scheduling where processing times satisfy dominancy and/or ordered relations, SPT rules are proved to be optimal.

A Time-Sharing Queue with a Finite Number of Customers

A time-sharing queue serving a finite number of customers is described. It is assumed that both the service time and the time elapsing between termination of service and the next arrival of the same customer at the queue (service station) are exponential. The model was studied by Krishnamoorthi and Wood, but their results are not in complete agreement with the results of this paper. In addition, some new results are presented in terms of steady-state expectations.

Scheduling on machines with variable service rates

Abstract This paper deals with scheduling on single and parallel machines where the service rate of a machine remains constant while a job is being processed and is changed upon its completion. Associated with machine M l there is a vector of service factors α l = ( α 1 l , α 2 l ,…,); it is described as cyclic of order k iff α 1 ( k ) = ( α 1 l ,…, α kl , α 1 l ,…,). Processing job J i in the j th position on M l consumes α jl t i time units. We present an 0( n log n ) algorithm for l/vsr/ C max and an 0( n m log n ) algorithm for Pm / vsr /∑ C i , m ⩾ 1. It is proved that l/vsr/ L max is NP-hard even for a monotone non-decreasing or a cyclic series of service factors, thus l/vsr/δ, δ ϵ {∑ U i , ∑ T i } are NP-hard as well. Finally, efficiently solvable special cases of l/vsr/δ, δ ϵ { L max , ∑ U i , ∑ T i } are studied.

Computer Time-Sharing Queues with Priorities

The paper deals with computer time-sharing disciplines in which external priorities are introduced. For a computer system under a time-sharing discipline, the following priority disciplines are discussed: (a) head-of-the-line; (b) preemptive repeat; and (c) mixed preemptive strategy. All models in question assume that customers arrive according to homogeneous Poisson processes, and that service times are mutually independent exponentially distributed random variables. Results are given in terms of steady-state expectations.

Cyclic Queues with Bulk Arrivals

This paper deals with a single-server station (a computer) where each customers demand comprises an independent random number of jobs (programs). Under certain assumptions, two cyclic disciplines are mathematically analyzed: (a) continuous job service—a round-robin discipline where the quantums length is distributed as the service requirement of a job; (b) intermittent job service—a double round-robin discipline—in the first instance in terms of the jobs within the customers demand, and in the second in terms of the customer himself.