A Comprehensive Study of an Online Packet Scheduling Algorithm

Abstract

We study the bounded-delay model for Qualify-of-Service buffer management. Time is discrete. There is a buffer. Unit-length jobs (also called packets) arrive at the buffer over time. Each packet has an integer release time, an integer deadline, and a positive real value. A packet's characteristics are not known to an online algorithm until the packet actually arrives. In each time step, at most one packet can be sent out of the buffer. The objective is to maximize the total value of the packets sent by their respective deadlines in an online manner. An online algorithm's performance is usually measured in terms of competitive ratio, when this online algorithm is compared with a clairvoyant algorithm achieving the best total value. In this paper, we study a simple and intuitive online algorithm. We analyze its performance in terms of competitive ratio for the general model and a few important variants.Keywords: online algorithm, competitive analysis, buffer management, packet scheduling Model DescriptionWe consider the bounded-delay model introduced in [1,2]. Time is discrete. The t-th (time) step presents the time interval (t−1, t]. There is a buffer and unit-length jobs (also called packets) arrive at the buffer over time. Each packet p has an integer release time r p ∈ Z + , an integer deadline d p ∈ Z + , and a positive real value v p ∈ R + . A packet p's characteristics are not known to an online algorithm until p actually arrives at the buffer at time r p . In each step, at most one packet in the buffer can be sent. A packet p is said to be successfully sent at time t if r p ≤ t ≤ d p . The objective is to maximize the total value of the packets that are successfully sent in an online manner.As people have noted, the offline version of this problem can be solved efficiently using the Hungarian algorithm [3] in time O(n 3 ), where n is the number of packets in the input instance.In the framework of competitive analysis which provides worst-case guarantees, an online algorithm's performance is measured in terms of competitive ratio [4]. For a maximization problem, an online algorithm is called c-competitive if for any finite instance, its total value is no less than 1/c times of what an optimal offline algorithm achieves. In competitive analysis, an input instance is allowed to be generated in an adversarial way so as to maximize the competitive ratio. The upper bound of competitive ratio is achieved by some online algorithms. A competitive ratio strictly less than the lower bound cannot be reached by any online algorithm. If an online algorithm has its competitive ratio same as the lower bound, we say that this online algorithm is optimal. For the bounded-delay model, the currently best known result is 2 √ 2 − 1 ≈ 1.828 [5] and the lower bound is (1 + √ 5)/2 ≈ 1.618 [1,6]. If an online algorithm decides which packet to send only based on the contents of its current buffer, and independent of the packets that have already been released and processed, we call it memoryless.In this paper, we study a sim...

A Universal Randomized Packet Scheduling Algorithm

“…Interestingly, one of the optimal deterministic algorithms for similarly ordered instances [16] performs well in several restricted instance classes [15] (the performance of the other algorithm [13] was not studied). Let us mention one class of instances, studied by Kesselmann et al in their seminal paper [14], for which our algorithm provides additional bounds: as various transmission protocols usually specify only several priorities for packets, it is sensible to bound the number of different packet weights.…”