We study the problem of scheduling activities of several types under the constraint that, at most, a fixed number of activities can be scheduled in any single time slot. Any given activity type is associated with a service cost and an operating cost that increases linearly with the number of time slots since the last service of this type. The problem is to find an optimal schedule that minimizes the long-run average cost per time slot. Applications of such a model are the scheduling of maintenance service to machines, multi-item replenishment of stock, and minimizing the mean response time in Broadcast Disks. Broadcast Disks recently gained a lot of attention because they were used to model backbone communications in wireless systems, Teletext systems, and Web caching in satellite systems.The first contribution of this paper is the definition of a general model that combines into one several important previous models. We prove that an optimal cyclic schedule for the general problem exists, and we establish the NP-hardness of the problem. Next, we formulate a nonlinear program that relaxes the optimal schedule and serves as a lower bound on the cost of an optimal schedule. We present an efficient algorithm for finding a near-optimal solution to the nonlinear program. We use this solution to obtain several approximation algorithms.(1) A 9/8 approximation for a variant of the problem that models the Broadcast Disks application. The algorithm uses some properties of "Fibonacci sequences." Using this sequence, we present a 1 57-approximation algorithm for the general problem.(2) A simple randomized algorithm and a simple deterministic greedy algorithm for the problem. We prove that both achieve approximation factor of 2. To the best of our knowledge this is the first worst-case analysis of a widely used greedy heuristic for this problem.1. Introduction. We study a problem of scheduling activities of several types over an infinite number of time slots. We describe the model in terms of a generalized version of the maintenance service scheduling problem studied in Anily et al. (1998). In this formulation, there are m machines 1 m that are to be scheduled for maintenance over an infinite discrete time horizon. In each time slot, at most M machines can be scheduled for maintenance. The cost of operating a machine at any given time slot depends on the number of time slots since the last maintenance of that machine. We assume that each machine i is associated with a constant a i > 0 and the cost of operating the machine in the hth time slot after the last maintenance of that machine is h + b a i , for h ≥ 0 and integer b ≥ 0. (The value of b is determined by the application.) We assume that the cost associated with the maintenance service of the ith machine is c i ≥ 0. The problem is to find an optimal schedule specifying at which time slots to maintain each of the machines to minimize the long-run average cost per time slot.More formally, a schedule for the Generalized Maintenance Scheduling Problem (GMSP) with m machines ...
Abstract-With increasing interest in energy constrained multi-hop wireless networks [2], a fundamental problem is one of determining energy efficient communication strategies over these multi-hop networks. The simplest problem is one where a given source node wants to communicate with a given destination, with a given rate over a multi-hop wireless network, using minimum power. Here the power refers to the total amount of power consumed over the entire network in order to achieve this rate between the source and the destination. There are three decisions that have to be made (jointly) in order to minimize the power requirement.• The path(s) that the data has to take between the source and the destination. (Routing) • The power with with each link transmission is done. (Power Control).• Depending on the interference or the MAC characteristics, the time slots in which specific link transmissions have to take place. (Scheduling) To the best of our knowledge, ours is the first attempt to derive a performance guaranteed polynomial time approximation algorithm for jointly solving these three problems. We formulate the overall problem as an optimization problem with non-linear objective function and non-linear constraints. We then derive a polynomial time 3-approximation algorithm to solve this problem. We also present a simple version of the algorithm, with the same performance bound, which involves solving only shortest path problems and which is quite efficient in practice. Our approach readily extends to the case where there are multiple sourcedestination pairs that have to communicate simultaneously over the multi-hop network.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.