Large profits or fast gains: A dilemma in maximizing throughput with applications to network processors

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Abstract

We consider the fundamental problem of managing a bounded size queue buffer where traffic consists of packets of varying size, each packet requires several rounds of processing before it can be transmitted out, and the goal is to maximize the throughput, i.e., total size of successfully transmitted packets. Our work addresses the tension between two conflicting algorithmic approaches: favoring packets with fewer processing requirements as opposed to packets of larger size. We present a novel model for studying such systems and study the performance of online algorithms that aim to maximize throughput.

Introduction

Over the recent years, there has been a growing interest in understanding the effects that buffer sizing has on network performance. The main motivation for these studies is to understand the interplay between buffer size, throughput, and queueing delay. Broadly speaking, one can identify three main types of delay that contribute to packet latency: transmission and propagation delay, processing delay, and queueing delay. Recent research that advocates the usage of small buffers in core routers, aiming to reduce queueing delay in the presence of (mostly) TCP traffic, sidesteps the issue that as buffers get smaller, the effect of processing delay becomes much more pronounced (Ramaswamy et al., 2009). The importance of these phenomena is further emphasized by increasing heterogeneity of network traffic processing. The modern network edge is required to perform tasks with ever-increasing complexity including features such as advanced VPNs services, deep packet inspection, firewall, intrusion detection etc. Each of these features may require a different processing effort at the routers (Wolf and Franklin, 2000), and such features directly affect processing delay. As a result, the processing method of packets and the way how these packets are processed (“run-for-completion”, processing with preemptions, etc.) may have significant impact on queueing delay and throughput; increasing the required processing per packet in some of the flows may cause increased congestion even for traffic with relatively modest burstiness characteristics.

We should note that in the general case, processing requirements are independent of packet lengths, thus decoupling the amount of work required for a router to process a packet from the throughput gained upon its successful transmission. Processing requirement and packet length are indeed two independent characteristics in the modern networks: a short packet may require complex processing policies while a long packet may simply go through almost untouched and vice versa. This independence lets us design processing policies better suited for different objective functions (e.g., by optimizing bytes transmitted per processing cycle).

This situation leads to several questions relevant to the design and implementation of router architectures. For instance, in light of heterogeneous processing requirements in the traffic, does one need to implement input buffering before a packet is handled by the network processor? If so, what should the size of such a buffer be, and what admission control policy should be applied? Another question is related to adapting common active queue management (AQM) policies so that they account for heterogeneous processing required by traffic. In this respect, the main question is whether current AQM approaches are capable of considering these characteristics; if not, what form should new policies take? In this work, we initiate the study of these questions and the tradeoffs they encompass. We focus on improving our understanding of effects that processing disciplines have on throughput in cases of bounded buffers where traffic is heterogeneous in terms of both packet processing requirements and packet length.

In what follows, we adopt the terminology used to describe queue management within a router in a packet-switched network. We focus our attention on a general model for the problem where we are required to manage the admission control and scheduling units in a single bounded size queue, where arriving traffic consists of packets, such that each packet is labeled with its size (e.g., in bytes), and processing requirement (in processor cycles). A packet is successfully transmitted once the scheduling unit has scheduled the packet for processing for at least its required number of cycles, while the packet resides in the buffer. If a packet is dropped from the buffer, either upon arrival due to admission control policies or after being admitted and possibly partially, but not fully, processed (in scenarios where push-out is allowed), such a packet is irrevocably lost. We focus our attention on maximizing the throughput of the queue, measured by the total number of bytes of packets that are successfully transmitted by the queue.

Section snippets

Our contributions

In this work we provide a formal model for studying problems of online buffer management and online scheduling in settings where packets have both varying size and heterogeneous processing requirements, and one has a limited size buffer to store arriving packets. Our model lets us study the interplay between potentially conflicting approaches, favouring large packets and favouring packets with less required processing, in the situation where the goal is to maximize the total length of

Related work

In recent years, there has been a surge in the study of the effects of buffer size on traffic queueing delays arising in networking systems. Appenzeller et al. (2004) studied this problem in the context of statistical multiplexing, focusing mostly on TCP flows. More recently, broader aspects of these question were studied, and a comprehensive overview of perspectives on router buffer sizing can be found in Vishwanath et al. (2009).

The works (Isaac Keslassy and Kogan, 2012, Kogan et al., 2016,

Model description and algorithmic framework

Consider a buffer with bounded capacity of B bytes handling the arrival of a sequence of packets. Each arriving packet p has a size (p){1,,L} (in bytes) and a number of required processing cycles r(p){1,,k}; both (p) and r(p) are known for every arriving p. Note that required processing characteristics on a network processor are often highly regular and predictable for a fixed configuration of network elements (Wolf et al., 2003), so per-packet processing requirements are expected to be

Useful properties of ordered multi-sets

To facilitate our proofs, we will make use of properties of ordered (multi-)sets. These notions, as well as properties we show they satisfy, will enable us to compare the performance of our proposed algorithms with the optimal policy possible, for various priority disciplines. In the following, we consider multi-sets of real numbers, where we assume each multi-set is ordered in non-decreasing order. We will refer to such multi-sets as ordered sets. For every 1i|A|, we will further refer to

Non-push-out policies

While non-push-out algorithms may have different priorities for the admission policy (which packets to admit from a set of simultaneously arriving packets), they cannot push already admitted packets out. As a result, the worst-case bounds are very similar for all three priorities we consider, and we simply prove a unified lower and upper bound on NPO performance for any admission policy.

Theorem 3

NPO is at least kL-competitive and at most k(L+1)-competitive.

Proof

We begin with the lower bound. To show a lower

Buffer management with SRPT priorities

In this section we address the buffer management problem of when the queueing discipline gives higher priority to packets with fewer required processing cycles. We show first a lower and then an upper bound for the PO Algorithm 2 with SRPT priorities. In this and subsequent sections we focus our attention on the push-out case since non-push-out results have already been shown in Section 6 for all considered priorities.

Theorem 4

For B>2L, PO is at least L-competitive for SRPT-based priorities.

Proof

Assume that B

Buffer management with LP priorities

We begin with a lower bound for the PO algorithm with LP-based priorities and then proceed to an upper bound of PO with LP-based priorities.

Theorem 11

PO is at least k-competitive for LP-based priorities on a sufficiently long sequence .

Proof

Here, we will consider a push-out version of OPT for simplicity of description. Assume BL be an integer value. Consider a cycle of L iterations of the first type and later sequence of n>0 iterations of the second type (defined below). Each iteration of the first type

Buffer management with MEP priorities

In this section we study the performance of a BM implementing PQ, where priorities are set in accordance with the non-increasing order of processing cycles divided by packet length. This priority is dubbed the Most Effective Packet first priority (MEP), or the effective-ratio priority. Recall that our objective here is to maximize the number of bytes transmitted in total. Non-push-out results are similar to Section 6.

The following theorem provides a lower bound on the performance of the

General remarks

In order to obtain a better understanding of the differences between our proposed solutions, we conducted a simulation study where we evaluate the performance of each policy in terms of throughput and address the effect of variable processing requirements on the average delay in the system.

Publicly available traffic traces (such as CAIDA) do not contain, to the best of our knowledge, information on the processing requirements of packets. Furthermore, these requirements are difficult to extract

Conclusion

Increasingly heterogeneous packet processing requirements in modern networks pose novel design challenges to NP architects. In this work we study the impact of two important characteristics, maximal required processing k and maximal packet size L, and show the significance of the relationship between k and L. We introduce three different priority regimes for processing: SRPT, LP, and MEP, and study their performance in queues with bounded buffers. We present results for both non-push-out, as

Acknowledgments

The work of Sergey Nikolenko was partially supported by the Government of the Russian Federation Grant 14. Z50.31.0030 and the Russian Presidential Grant for Young pH. D.s MK-7287.2016.1. The work of Gabriel Scalosub was supported by the Israel Science Foundation (Grant no. 1036/14). Work by Michael Segal has been supported by Israel Science Foundation (Grant no. 317/15), by IBM Corporation and by Israel Ministry of Economy and Industry.

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