Bounds for optimal flow control window size design with application to high-speed networks

✍ Scribed by Redha M. Bournas

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 672 KB
• Volume: 332
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(95)00033-t

✦ Synopsis

In this paper, we study the problem of optimal window size design that arises in flow control of communications protocols. We consider both the sliding and pacing window flow control mechanisms. We address the case of one data transfer session between a sender and a receiver. The assumption is that the sending station is transmitting a large volume of data in a burst to the receiving station. There are no restrictions on the distribution of arrival or service times at the intermediate packet switchiny stations in the communication path connecting the sender and receiver. Our criterion for optimal window size design is the maximization of the network power. We derive upper and lower bounds of the optimal window size that depend on the network performance characteristics. The main result of this paper is that the upper bound is a simple function of the number of hops, the round trip propagation delay, and the maximum throughput of the communication path. Our analysis and results incorporate the round trip propagation delay which may be very important in the design of window sizes for high-speed networks. This work could be applied to a Transmission Control Protocol ( TCP) connection over a Wide Area Network (WAN), or to a virtual Advanced Peer to Peer Networking (APPN) session.

authors ; see (lqi)

. There, the authors made assumptions on the inter-arrival times distribution of exogenous traffic at the intermediate packet switching nodes, and the packet service times distribution at all the nodes. Based on these assumptions, the optimal window size design becomes mathematically tractable, although still difficult to analyze. In these papers, the authors give us some insight on the mathematical techniques used, and the optimal window size values as well. However, due to the emergence of high-speed networks and multimedia applications, the above assumptions no longer hold. This is because multimedia applications generate bursty traffic (which is no longer Poisson), and high-speed networking technology is based on transmitting packets of a given equal size (cells). But then the assumption of generally distributed arrivals at the intermediate packet switching nodes (which implies that the packet delay at each intermediate station is generally distributed) makes the optimal window size design problem mathematically not tractable. In this paper, we rather approximate the optimal window size by deriving upper and lower bounds. Both these bounds are functions of the network performance characteristics: the processing delay at each node, the capacity of each link, and the round trip propagation delay. In particular, we express the upper bound as a simple function of the number of hops, the round trip propagation delay, and the maximum throughput of the communication path. We note that the round trip propagation delay may no longer be negligible due not only to the high-speed of physical network media (fiber), but to the implementation of very advanced (fast) hardware technologies in the switching nodes also. Under assumptions on the arrival and service times distributions, the authors in (6) derived an expression for the optimal sliding window size that incorporates the round trip propagation delay. It is shown in (6) that if this delay were too small relative to the transmission and switching station delays, then the optimal window size reduces to the one developed in (2). The upper bound of the optimal window size derived herein under no assumptions on the arrival and service times distributions is a multiplicative factor of the particular result of (6).

The rest of the paper is organized as follows. In Section 2.1, we derive an upper bound on the data transfer session average throughput. In Section 2.2 we derive an upper bound of the network power as well. In Section 2.3, a lower bound on the data transfer session average throughput and a lower bound on the network power are derived. In Sections 2.4 and 2.5, we derive lower and upper bounds for the optimal window size. We finally conclude the paper in Section III.

I1. Optimal Window Size Design

In this section, we study the process of transmitting data from a sender to a receiver along a given path as a queueing process. There are intermediate packet switching nodes in the path connecting the sending and receiving stations. We determine upper and lower bounds of the optimal window size (a number of packets), and quantify the corresponding throughput bounds.

Window flow control analysis has been done in the past ; see for example (1-4). However, the authors assume Poisson arrivals and exponential service times at each node, and that all nodes have the same average service rate. These assumptions