Scheduling Packets with Values and Deadlines in Size-Bounded Buffers

Abstract

Motivated by providing quality-of-service differentiated services in the Internet, we consider buffer management algorithms for network switches. We study a multi-buffer model. A network switch consists of multiple size-bounded buffers such that at any time, the number of packets residing in each individual buffer cannot exceed its capacity. Packets arrive at the network switch over time; they have values, deadlines, and designated buffers. In each time step, at most one pending packet is allowed to be sent and this packet can be from any buffer. The objective is to maximize the total value of the packets sent by their respective deadlines. A 9.82-competitive online algorithm has been provided for this model (Azar and Levy. SWAT 2006), but no offline algorithms have been known yet. In this paper, We study the offline setting of the multi-buffer model. Our contributions include a few optimal offline algorithms for some variants of the model. Each variant has its unique and interesting algorithmic feature. These offline algorithms help us understand the model better in designing online algorithms. * Research is partially supported by NSF grant CCF-0915681. † Department of Computer Science, George Mason University, Fairfax, VA 22030, USA. lifei@cs.gmu.edu IntroductionMotivated by providing quality-of-service differentiated services in the Internet, we consider buffer management algorithms for network switches. We study a multi-buffer model. A network switch consists of m size-bounded buffers Q 1 , Q 2 , . . ., Q m ; their sizes are denoted as B 1 , B 2 , . . . , B m respectively. At any time, the number of packets residing in each individual buffer Q i cannot exceed its capacity B i . Time is discretized into time steps. Packets arrive at the network switch over time and each packet p has an integer arriving time (release time) r p ∈ R + , a non-negative value v p ∈ R + , an integer deadline d p ∈ Z + , and a designated buffer b p ∈ {Q 1 , . . . , Q m } that it can reside in. The deadline d p specifies the time by which p should be sent. This model is preemptive such that the packets already existing in the buffers can be dropped at any time before they are transmitted. A dropped packet cannot be delivered any more. In each time step, at most one pending packet is allowed to be sent and this packet may be from any buffer. The objective is to maximize weighted throughput, defined as the total value of the packets transmitted by their respective deadlines.The first QoS buffer management model is introduced in [1]. Since then, quite a few researchers have studied this model as well as other variants, mostly in the online settings [7,6,3,8,5]. A well-studied model is called the bounded-delay model. In this model, there is only one buffer. Packets have integer release time, integer deadlines, and non-negative values. The objective is to maximize the total value of the packets sent by their deadlines. An implicit assumption on this model is the buffer's sufficiently large size. All released packets can be stored ...