Elsevier

Computer Communications

Volume 35, Issue 4, 15 February 2012, Pages 431-443
Computer Communications

Analysis of minimal backlogging-based available bandwidth estimation mechanism

https://doi.org/10.1016/j.comcom.2011.11.011Get rights and content

Abstract

This paper analyzes the minimal backlogging-based available bandwidth estimation mechanism to strengthen the theory behind the mechanism. The minimal backlogging method estimates the available bandwidth using the statistic of the probing traffic service rate. We show that the statistic of the probing traffic service rate is a consistent estimator of the available bandwidth for a G/G/1 queueing system under minimal backlogging condition to support the minimal backlogging method theoretically. In order to emulate the minimal backlogging method in a real multi-hop network, we detect the minimal backlogging condition or closeness of the probing rate to the available bandwidth based on the busy period length, and change the probing rate adaptively to maintain the minimal backlogging condition. We explain that the minimal backlogging condition or available bandwidth might be detected more accurately by the busy period of probing packets than by the gap response curve or rate response curve, and enhance the minimal backlogging method further by introducing a new initial probing rate estimation mechanism. A reasonable range of available bandwidth for a short time interval can be obtained using the mean and variance of the estimated available bandwidth, since the proposed mechanism can estimate the available bandwidth quickly and track it adaptively. The proposed mechanism is implemented in a Linux environment. The performance of our scheme is compared to those of conventional available bandwidth estimation mechanisms through experiments on a test-bed with single-hop or multiple-hop topologies.

Introduction

The reliable estimation of available bandwidth for a network path is crucial for high utilization of network resources, as well as QoS guarantee for real-time flows. If the available bandwidth (AB) for a specific network path is known to a traffic source node, the source node might avoid congested paths [1] or the information about AB can be used for capacity provisioning, network troubleshooting, traffic engineering (TE), admission control, and end-to-end QoS provisioning [2], [3], [4], [5]. Thus, reliable AB monitoring is crucial to exploit network resource efficiently.

For a network path P between a node pair consisting of H serially connected links, AB Ca for the path is usually defined asCa=min1iHCi(1-ui),where Ci and ui are the link rate and the utilization of the ith link, respectively. The link with the least unused bandwidth of Ca is referred to as the tight link. The link with the minimum link rate is referred to as the narrow link.

Many schemes have been proposed to estimate the end-to-end available bandwidth [6], [7], [8], [9], [10], [11], [12], [13]. The underlying principles of most of these methods can be classified into two categories: probe gap model (PGM) and probe rate model (PRM). In the probe gap model, a probe packet pair is usually sent to the destination node. When Δin and Δout are the inter-packet gaps just before and at the tight link, respectively, if we know the link rate of the tight link C, then the rate of cross-traffic is C(Δout  Δin)/Δin, and the available bandwidth isCa=C1-Δout-ΔinΔin.Spruce [12], Delphi [7], and IGI [11] are based on this PGM. However, this result is justified only under the fluid cross-traffic model [14], [15].

Melander et al. [8] investigated the relationship between the input probing rate (rI) and the output probing rate (rO) of a single node and showed the following relationship under the First-In First-Out (FIFO) fluid model:rO=rI,rI<C-λ,CrIrI+λ,rIC-λ,where C and λ are the link rate and the cross-traffic rate, respectively. On the multiple hop path, the relationship between rI and rO is maintained if rI is less than the second smallest available bandwidth on the path under the same fluid model. Thus, if we find the value of rI above which the ratio of rI/rO is greater than 1, that value of rI corresponds to the available bandwidth by the model of (2). This available bandwidth detection principle is called PRM, and TOPP [8], PTR [11], pathload [9], and pathchirp [10] are based on this idea. TOPP and PTR search the point where the value of rI/rO diverges from 1 using the concept of linear search. Pathload finds the range of the available bandwidth using the binary search concept. Although other PRM methods use packet pairs or equally spaced packet trains, pathchirp uses packet trains with exponentially decreasing inter-packet spacing and calculates the available bandwidth based on the queueing pattern of the arriving packets. Liebeherr et al. [16] analyzed pathload and pathchirp by interpreting available bandwidth estimation as a problem in min-plus linear systems under the idealized fluid-flow traffic assumption.

Thus, most existing methods are based on either PGM or PRM. In this paper, we investigate a different available bandwidth estimation methodology, termed the minimal backlogging method. We proposed the minimal backlogging method to estimate the end-to-end available bandwidth in [13]. The mechanism of [13] estimates the available bandwidth using the statistic of the probing traffic service rate when the probing packets are sent according to the minimal backlogging method. However, the convergence of the statistic was not proved in [13]. Thus, to strengthen the theory for the minimal backlogging method, we show that the statistic of probing traffic service rate is a consistent estimator of the available bandwidth for a G/G/1 queueing system under the minimal backlogging condition. Another issue related to the original version of the minimal backlogging method is the convergence time might be increased if the gap between the initial probing rate and the available bandwidth is large. We propose a new initial probing rate estimation scheme to reduce the gap between the initial probing rate and the available bandwidth. The enhanced version of the minimal backlogging method is implemented in a Linux environment and compared to conventional available bandwidth estimation tools. We also investigate the advantage of busy period length-based minimal backlogging condition detection over available bandwidth detection based on the gap or rate response curve used in PGM or PRM. Thus, the contributions of this paper can be summarized as follows:

  • We show that the statistic of the probing traffic service rate under minimal-backlogging condition is a consistent estimator of the available bandwidth for a G/G/1 queueing system.

  • We show that the minimal backlogging condition can be checked based on the busy period length through analysis and simulation.

  • We show that the minimal backlogging-based available bandwidth estimation mechanism has higher accuracy than conventional available bandwidth mechanisms, especially when the cross traffic load changes dynamically on a multi-hop path due to the busy period length-based minimal backlogging condition detection and a new initial probing rate estimation scheme.

The remainder of this paper is organized as follows. We first discuss related work in Section 2. In Section 3, we explain the minimal backlogging method and the statistic, probing traffic service rate, used to estimate the available bandwidth of a queueing system. We show that the above statistic is a consistent estimator of the available bandwidth for a G/G/1 queueing system under the condition that the probing packets are sent by the minimal backlogging method. In Section 4, we explain how the minimal backlogging method is adapted in a realistic environment and the advantage of detecting the minimal backlogging condition based on busy period length is described. In Section 5, we introduce a simplified path model for multiple hop paths. The approach for a single server is extended to multiple hop paths using the simplified path model, and we also propose a new initial probing rate estimation scheme. In Section 6, the performance of the proposed available bandwidth estimation mechanism is evaluated by experiments on a test-bed with a single-hop or multiple-hop network topology. Finally, conclusions are presented in Section 7.

Section snippets

Related work

C-probe [6] was the first attempt to measure available bandwidth. C-probe estimates the available bandwidth from the dispersion of trains of eight packets. A similar approach was taken in pipechar [17]. They assumed that the dispersion of long packet trains is inversely proportional to the available bandwidth. However, Dovrolis et al. [18] showed that this is not true. The dispersion of long packet trains does not measure the available bandwidth in a path, but measures a different throughput

Estimation of available bandwidth for a single server

Before considering the AB estimation problem for multiple hop routes, we introduce some concepts and theory for a single server. We consider a queueing system with a First-Come-First-Served (FCFS) service policy. Fig. 1 shows a queueing system of interest. The service rate is C (bits per second), and the arrival rate of packets, except probing packets, is λ (packets per second). Suppose that the service time of a packet is given by the packet size divided by the service rate C of the system.

Detection of minimal backlogging condition based on busy period length

We showed that the available bandwidth of a single server system can be estimated reliably if the probing traffic can be sent according to the minimal backlogging method in the previous section. However, it is not easy to realize the ideal minimal backlogging method even for a single server in a real environment. The access delay between the probing system and the target single server cannot be zero in a real networking environment, and thus, the next probing packet cannot arrive exactly at the

Estimation of available bandwidth for a multiple hop path

The AB estimation mechanism for a single server developed in the Section 3 cannot be directly applied to AB estimation for a network path between a specific node pair, because a network path usually consists of multiple hops. Thus, we employ a simplified path model [13] and attempt to satisfy the minimal backlogging condition by changing the probing traffic rate adaptively to extend the AB estimation theory for a single server to a multiple-hop environment. The simplified path model and the

Performance evaluation

We implemented the enhanced version of minimal backlogging method in a Linux environment. We evaluate the performance of the proposed scheme through experiments on a test-bed. Since pathload and pathchirp are known as the most accurate available bandwidth estimation tools [28], [29], the proposed scheme is compared to these tools and another well-known tool called spruce, which is based on PGM, in terms of accuracy and overhead.

Conclusions

In this paper, we analyzed the minimal backlogging-based available bandwidth estimation mechanism to strengthen the theory behind the mechanism and find the advantage of detecting the minimal backlogging condition based on the busy period of probing packets. If the minimal backlogging condition is maintained for a single server, then the available bandwidth of the server can be estimated by the statistic of probing traffic service rate, i.e. the ratio of the amount of probing packets served to

Acknowledgement

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-313-D00641).

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