Maematical and Computational Applications, Vol. 4, No., pp. 65-72, 29. Association for Scientific Research AN ACTIVE QUEUE MANAGEMENT ALGORITHM OR REDUCING PACKET LOSS RATE Babek Abbasov Department of Computer Engineering Qafqaz University, Baku, Azerbaijan babek@qafqaz.edu.az Serdar Korukoğlu Department of Computer Engineering Ege University, 35 Bornova, Đzmir, Turkey serdar.korukoglu@ege.edu.tr Abstract-Among various active queue management schemes AQM, random early detection RED is probably e most etensively studied. Unlike e eisting RED enhancement schemes, we use hazard rate estimated packet dropping function in RED. We call is new scheme HERED. The underlying idea is at, wi e proposed packet dropping function, packet dropping becomes gentler an RED at light traffic load but more aggressive at heavy load. Simulations demonstrate at HERED achieves a higher and more stable roughput and performs better an current active queue management algorims due to e lowest packet drops. Keywords- Active Queue Management, Congestion, Random Early Marking, Hazard unction.. INTRODUCTION Congestion control is one of e most important problems in e Internet. Most of e eisting Internet routers play a passive role in congestion control, and are known as droptail routers. A droptail router discards packets when its IO queue is full. It was shown in Zhang et al. [] at under heavy load conditions, droptail routers cause global synchronization, a phenomenon in which all senders sharing e same bottleneck router/link shut down eir transmission windows at almost e same time, ereby causing a sharp drop in e bottleneck link utilization. It was also found in Mahajan et al. [2] at droptail routers are biased against bursty sources. This is because, when a burst of packets from a sender arrives at a fully occupied queue, a sustained packet drop wiin e same window of data occurs. Research in loyd et al. [3] and u and Ansari [4] showed at e dominant transport layer protocol, transmission control protocol TCP [5], lacks e ability to recover from such multiple packet losses wiin e same window of data. Therefore, e TCP sender has to rely on retransmission timeouts to recover e lost packets. Retransmission timeout significantly slows down e transmission rate of a TCP flow, because almost no data will be sent when e sender waits for e retransmission timer to epire. A good congestion control scheme should erefore avoid triggering unnecessary timeouts.
66 B. Abbasov and S. Korukoğlu On e oer hand, as more and more multimedia applications running on top of UDP are being deployed, e traditional approach of relying solely on TCP s end-to-end congestion control algorims will no longer be viable [6]. The network, in particular e routers in e network, should play an active role in its resource allocation, so as to effectively control/prevent congestion. This is known as active queue management AQM [7]. The essence is at an AQM router may intelligently drop packets before e queue overflows. Among various AQM schemes, Random Early Detection RED [8] is probably e most etensively studied. RED is shown to effectively tackle bo e global synchronization problem and e problem of bias against bursty sources. Due to its popularity, RED or its variants has been implemented by many router vendors in eir products. or eample Cisco implemented using weighted random early detection WRED. On e oer hand, ere is still a hot on-going debate on e performance of RED. Some researchers claimed at RED appears to provide no clear advantage over droptail mechanism [9]. But more researchers [2 ] acknowledged at RED shows some advantages over droptail routers but it is not perfect, mainly due to one or more of e following problems. RED performance is highly sensitive to its parameter settings []. In RED, at least 4 parameters, namely, maimum reshold ma, minimum reshold min, maimum packet dropping probability ma p, and weighting factor w q, have to be properly set. RED performance is sensitive to e number of competing sources/flows. RED performance is sensitive to e packet size. Wi RED, wild queue oscillation is observed when e traffic load changes. As a result, RED has been etended and enhanced in many different ways [2 ]. It can be found at a common underlying technique adopted in most studies is to steer a router to operate around a fied target queue size which can eier be an average queue size or an instantaneous queue size. There are some concerns on e suitability of is approach, since e schemes us designed are usually more complicated an e original RED. This renders em unsuitable for backbone routers where efficient implementation is of primary concern. In some schemes, additional parameters are also introduced. This adds etra compleity to e task of parameter setting. Unlike e eisting RED enhancement schemes, we propose to simply replace e hazard rate estimated packet dropping function in RED. The rest of e original RED remains unchanged. We call is new scheme HERED. The underlying idea is at, wi e proposed nonlinear packet dropping function, packet dropping is gentler an RED at light traffic load but more aggressive at heavy load. Therefore, at light traffic load NLRED encourages e router to operate in a range of average queue sizes raer an a fied one. When e load is heavy and e average queue size approaches e maimum reshold ma an indicator at e queue size may soon get out of control, HERED allows more aggressive packet dropping to quickly back off from it. Simulations demonstrate at NLRED achieves a higher and more stable roughput an RED and oer efficient variants of RED. Since HERED is fully compatible wi RED, we can easily upgrade/replace e eisting RED implementations by HERED.
An Active Queue Management Algorim for Reducing Packet Loss Rate 67 2. THE HAZARD UNCTION The hazard function is e conditional density function of failure at time t, given at e unit has survived until time t. Therefore, letting denote e random variable and denote e realization, { } [ ], lim lim lim lim f P h f + + + + It turns out at specifying a hazard function completely determines e cumulative distribution function and vice-versa. 2.. The ailure Rate for e Weibull Distribution or e Weibull distribution, e hazard function is / / / / e e f h 2 Note at if e Weibull hazard function is constant. This should be no surprise, since for e Weibull distribution reduces to e eponential. When >, e Weibull hazard function increases, approaching as. Consequently, e Weibull is a fairly common choice as a model for components or systems at eperience deterioration due to wear-out or fatigue. or e case where <, e Weibull hazard function decreases, approaching as. or comparison purposes, note at e hazard function for e gamma distribution wi parameters r and λ is also constant for e case r e gamma also reduces to e eponential when r. Also, when r > e hazard function increases, and when r < e hazard function decreases. However, when r > e hazard function approaches λ from below, while if r < e hazard function approaches λ from above. Therefore,
68 B. Abbasov and S. Korukoğlu even ough e graph of e gamma and Weibull distributions look very similar, and ey can bo produce reasonable fits to e same sample of data, ey clearly have very different characteristics in terms of describing survival or reliability data. inally we can simplify hazard function for Weibull distributions as c h c. igure illustrates h function igure. Hazard function for e Weibull distribution 3. RELATED WORKS Lots of proposed queue management schemes are RED oriented. The difference of ese schemes is mainly in e parameter-adjusting meod. Their mechanisms for adaptation of dropping-probability in response to network condition are different. In is section, brief descriptions of ese queue management schemes are given. These representative queue management schemes include droptail RED [8], BLUE [], REM [2], SRED [3], and DRED [4]. or droptail, arrival packets are dropped when queue overflow occurs. Droptail incurs large queue leng and high packet loss rate at congested links. Especially, droptail results in a phenomenon, called global synchronization [4], when a lot of TCP flows compete in a bottleneck. The total roughput of TCP flows decreases when global synchronization occurs. It is really a simple queue management and does noing to prevent congestion. However, droptail is e most widespread queue management scheme due to its simplicity. Random early detection is a queue management scheme at is intended to remedy e shortcomings of droptail. RED implicitly notifies one of sources of congestion by randomly dropping an arriving packet. The selected source is informed by e packet loss and its sending rate is reduced accordingly. Consequently, congestion is alleviated. The dropping probability of RED is decided by e queue leng. An arriving packet may be dropped before e queue is full. It is an early congestion notification. The dropping probability is a function of average queue leng. When e queue occupancy grows, congestion builds up. Then, e dropping probability increases in order to provide enough early congestion notifications.
An Active Queue Management Algorim for Reducing Packet Loss Rate 69 The RED dropping probability function is a piece-wise linear function. It is defined by a triplet min, ma, p ma. Upon a packet arrival, e packet is admitted into e queue if e average queue leng q a is less an min, or is dropped if larger an ma. If q a is between min and ma, e arrival packet is randomly dropped wi e probability defined by a linear function evaluated at q a. However, queue leng is not a good indicator of severity of congestion and issues of congestion notifications may be too bursty, leading to ecessive loss, or too mild, failing to stop congestion building. Several queue management schemes, such as BLUE, REM, SRED, and DRED, were proposed to improve e performance of RED. BLUE uses queue leng and link utilization as indicators of traffic load and congestion. Drop rate is adjusted by e indicators. If e current queue size eceeds a predetermined reshold L, dropping probability is raised by a very small fied amount d. Conversely, if e link is idle, dropping probability is reduced by a small fied amount d 2.The parameters d and d 2 are configurable for BLUE. To avoid aggressive packet dropping, BLUE keeps a minimum interval, called freeze time, between two successive updates. However, if dominant round-trip time RTT of flows or number of flows rough e queue changes, e parameter settings may not be suitable and queue leng oscillates. To deploy Random Eponential Marking REM, routers must perform eponential marking and sources must be REM aware. REM gives no incentive to cooperative sources. urermore, a properly calculated and fied design control constant must be known globally. Stabilized RED estimates number of flows and adapts dropping probability accordingly. The estimation is mainly based on a zombie list which first initializes e Hit parameter equal to and creates an empty list. Source destination addresses of each incoming packet are stored in e list. Once e list is full, an entry is randomly chosen from e list for each subsequent packet arrival, and its content is compared wi ose of e newcomer packet. If ere is a match, Hit is set to. Oerwise, Hit is set to, and wi a certain probability, e content of is entry may be replaced by e source destination addresses of e newcomer packet. By is match mismatch way, an approimate number of flows are estimated. However, e estimation converges very slowly and is heavily dependent on e size of zombie list. The estimated number of flows in SRED is inaccurate in most of time in a varied network environment. 4. HERED ALGORITHM We make some major changes to e RED algorim and call e new algorim HERED. An important advantage of our algorim HERED is at one can change e probability value p via e use of e hazard function c h c. Let T and q len denote e target value and e queue leng, respectively. In order to stabilize e queue leng against high congestion levels, we use c3, c2 and again c3 in e hazard function for e cases where min < q len < T, T < q len < ma and ma < q len < 2*ma, respectively. The pseudo code for HERED algorim is illustrated in igure 2.
7 B. Abbasov and S. Korukoğlu for each packet arrival calculate new prop probability p using hazard fuction h c c- : if qlen< min c no drop else if qlen< T min c 3 calculate probability p a : wi probability p a : mark e arriving packet else if T qlen< ma c 2 calculate probability p a : wi probability p a : mark e arriving packet else if ma qlen< 2 * ma c 3 calculate probability p a : wi probability p a : mark e arriving packet else if qlen 2 * ma mark e arriving packet igure 2. Pseudo code for HERED algorim. 5. SIMULATION RESULTS In is section, we compare e simulation results of our proposed HERED wi e eisting queue management schemes, REM and RED. All simulations are performed using NS-2 simulator. In all of our simulations, we use e topology shown in igure 3, which consists of n senders and one sink, connected togeer via router N, wi one of e queue management schemes. S n denotes e source of TCP flows. By varying flow number in each source S n, we produce different levels of traffic load and us different levels of congestion on e bottleneck link. N has a queue buffer size of 5 packets. The parameters used for e simulations are presented in Table. In e simulations, to 2 TCP sources are run for seconds from all nodes in S, S 2 Sn to e destination node D. igure 4 illustrates Loss Rate of RED, REM and HERED algorims. It is obvious at HERED has e lowest packet drops.
An Active Queue Management Algorim for Reducing Packet Loss Rate 7 S S 2 N D S n igure 3. Simulation topology. Table. Simulation Parameters Algorim Parameter Settings RED min 5, ma 5, 3 min, w q.2, ma p /5, as recommended in RED [3], gentle version used REM φ., γ., w q.2 HERED min 5, ma 5, 3 min, w q.2, ma p /5.4.35 HERED RED REM.3 Loss Rate.25.2.5..5 2 4 6 8 2 4 6 8 2 Simulation Time Seconds igure 4. Loss Rate of RED, REM and HERED algorims.
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