Micha Hofri

Disk scheduling: FCFS vs.SSTF revisited

We report on a rather extensive simulation effort directed at evaluating the merits of two scheduling strategies, FCFS and SSTF, for moving-arm disks under stationary request arrival process. For First-Come-First-Served (FCFS) scheduling, analytic results for the mean waiting time are also given (in a closed form). If the objective of a schedule is to minimize the mean waiting time (or queue size) and its variance, the results seem to confirm the overall superiority of Shortest-Seek-Time-First (SSTF), particularly for medium and heavy traffic. This holds also when the input is highly correlated or addresses the cylinders nonuniformly. These results contradict some statements published in recent years. The domain of policies where SSTF is optimal is considered. The simulation methodology is described in some detail.

Analysis of a stack algorithm for random multiple-access communication

An exact analysis is given of the main parameters that characterize the properties of the Capetanakis-Tsybakov-Mikhailov collision resolution algorithm with the free-access (continuous input) protocol. In particular, the distributions of the collision resolution interval, the delay experienced by a packet, and the state of the top level of the stack that is maintained by the algorithm are determined.

On the optimal control of two queues with server setup times and its analysis

Two queues are fed by independent, time-homogeneous Poisson arrival processes. One server is available to handle both. All service durations, in both queues, are drawn independently from the same distribution. A setup time is incurred whenever the server moves (switches) from one queue to the other. We prove that in order to minimize the sum of discounted setup charges and holdings costs, assumed linear in queue length and having the same rate at the two queues, the service at each queue should be exhaustive, A “threshold policy” is defined as a policy under which the server switches (from an empty queue) only when the other reaches a critical size. It is shown to be a likely candidate for the optimal policy, both for the discounted version and for the long-time average criterion.The steady-state performance of this policy (under somewhat more general distributional assumptions) and the optimal thresholds are determined for a number of cases.

A stochastic model of bin-packing

Recent research in combinatorial bin-packing models is extended to a stochastic model in which an arbitrary distribution of piece sizes is assumed. The asymptotic expected bin occupancy is obtained for a simple on-line algorithm. Convergence properties are also presented so that, for a given set of pieces, this measure can be related to the expected number of bins required relative to an optimization rule.

On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel

We analyse a stack protocol of the Capetanakis-Tsybakov-Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a noncommutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration semigroup we show that for arrival rates smaller than a fixed threshold, the mean CRI duration for n initial colliders is asymptotically proportional to n. Ergodicity conditions are also demonstrated.

Packet delay under the golden ratio weighted TDM policy in a multiple-access channel

Consider n transmission stations sharing a single communication channel. Packets arrive at the stations according to n independent renewal processes, possibly with different rates. The transmitters are assumed to be able to store an unlimited number of packets in their buffers. The stations transmit packets during time slots allocated to them according to a given {\em conflict-free distributed protocol.} The cost criterion according to which protocols are evaluated is the long-run weighted average buffer occupancies. (The average waiting time is a special case of such a weighting.) A lower bound to the cost criterion under time division multiplexing (TDM) protocols is given, and the costs of two protocols are analyzed. The first protocol is the {\em random-control} policy, and the second is the {\em golden ratio} policy which is shown to achieve a cost close to the lower bound for realistic parameters.

On the Expected Performance of Scanning Disks

This paper describes and analyzes the SCAN policy, used to schedule read/write requests at a moving-arm disk device, when fast response over the entire disk area is at a premium. An analysis is presented which handles precisely the dependence structure between queues accumulated at different cylinders. The arrival process of requests to each cylinder is assumed Poisson and homogeneous in time. A relatively efficient algorithm for evaluating numerically the mean waiting time at each cylinder is presented and its complexity analyzed. We discuss further extensions intended to capture additional details of realistic situations. These include distributed record lengths, skipping unreferenced cylinders and letting successive arrivals’ target cylinders be dependent variables.

Queueing models of secondary storage devices

Queueing theory has occupied an important role in the analysis of computer storage structures and algorithms. In this survey we focus on secondary or auxiliary storage devices, which often comprise the principal bottleneck in the overall performance of computer systems. We begin with descriptions of the more important devices, such as disks and drums, and a general discussion of related queueing models. Server motion and dependent successive services are salient features of these models. Widely used, generic results are presented and then applied to specific devices. The paper concludes with a discussion of open problems.

Should the two-headed disk be greedy? - Yes, it should

Abstract We consider a disk with two movable arms, each of which can access all of its surface. Read/write requests arrive singly and are treated as they arrive (no queue is formed). The arms can move concurrently, but not transmit simultaneously. We show that the policy that minimizes the mean seek time is to move to the required address the arm that is closest to it, while the other arm jockeys for optimal anticipatory position. This remains true when successive addresses are dependent and/or have different distributions.

Two-dimensional packing: expected performance of simple level algorithms

The packing of rectangles with both dimensions i.i.d. ∼U(0, 1) onto a semi-infinite fixed-width strip is considered. The expected efficiency, expressed in terms of unused area on the strip is calculated for three simple procedures, all of which are level-algorithms: Next Fit, Rotatable Next Fit (where pieces are possibly orientated before packing, so that their width always exceeds their height), and Next Fit Decreasing (pieces are presorted by their height). It becomes evident that the single most important determinant of this efficiency is the variance of level heights, and the procedures can be ranked by their success in keeping this variance down. It is indirectly demonstrated that worstcase behavior of simple packing algorithms is a poor predictor of their expected performance. Results were obtained via analysis, computer (symbolic) integration, and simulation.