Communications and Network, 2013, 5, 444-447 http://dx.doi.org/10.4236/cn.2013.53B2082 Published Online September 2013 (http://www.scirp.org/journal/cn) Copyright © 2013 SciRes. CN Limited Delay Preem ption Based Priority in D i fferen tiated Optical Burst Switching Network s with S m al l Buffers Jiuru Yang, Hong’an Ye Key Lab of Electronics Engineering, College of Heilongjiang Province, Heilongjiang University, Harbin, China Email: yangjr@hlju.edu.cn Received June 2013 ABSTRACT The composite scheme based on preemption and small buffers is an efficient method for contention resolution. To sup- port services differentiation, it is the first time that the analytical model of delay preemption based priority is built. Fu r- ther, in order to guarantee the low-loss requirement for high priority bursts, an improved scheme is proposed and inves- tigated by limiting the b uffered right of low priority bursts within the specific traffic states. The simulation results show that, without the deterioration of blocking performance, there is more than 40% reduction on burst loss being achieved under the condition ρ = 1.0 fo r high priority bursts. Keywords: Optical Burst Switching; Preemption; Small Buffers; Blocking 1. Introduction Since the concept of optical burst switching (OBS) is proposed by Qiao in 1999, it has been regarded as one of promising solutions for future optical Internet [1]. In OBS, due to one-way reservation behavior, the contention among bursts is inevitable, and much works have been dedicated to contention resolution by means of tunable wavelength converters (TWCs) and optical buffers, i.e., fiber delay lines (FDLs) [2-4]. However, it is determinate that the abundant usage of TWCs and FDLs at core nodes will bring the problems of not only the huge complexity in configuration, but also the large energy consumption be- cause of the astonishing traffic increase recently [5]. Under the wave of green networks, some practical and applic able sch emes bas ed small buffers (the leng th is about tens of packets) are concerned. In [6,7], the cost-effi- ciency based feedback buffer configuration is studied. Centering real-time and TCP traffic, the effects of size of small buffers on data loss are analyzed by Rouskas [8]. And to avoid burst-discarding, preemption is introduced through pre-reserving or post-reserving channel for the collided and buffered bursts [9,10]. Alternatively, [11] mitigates the performance degradation resulting from small buffers by smoothing traffic burstiness at edge nodes. Also, combine pre-reservation and segmentation, the au- thors proposed delay preemption to further reduce the packets loss probability of OBS [12]. In this paper, to support services differentiation, it is the first time that the analytical model on delay preemption based pr iority (DPP) is built. Moreover, on the basis of DPP, an improved scheme called Limited Delay Preemption Based Priority (LDPP) is proposed to guarantee the quantity of service (QoS) requirements of both mission-critical and delay- sensitive services by constraining the right of low priori- ty bursts to enter FDLs within the specific traffic states. 2. Analytical Model of Delay Preemption Based Priority Assuming the mean arrival rate and service time of bursts are λ and 1/μ, respectively. And the incoming packets with the common destinations are aggregated into a burst at edge nodes. For simplicity, the aggregated threshold in length Lb for all bursts is the same and fixed. In delay preemption with single-class, when more than two bursts transmit and switch in the same wavelength channel si- multaneously, a channel contention occurs. Given the FDLs is idle, the contended burst can be buffered and preempt the channel in advance [12]. We then define ρ = λ/Wμ is offered load and PD de- notes the total burst loss probability, where W is the number of wavelength in each fiber link. Thus, the prob- ability of channel usage at core nodes can be represented as (1) Likewise, in two-class system, we define both mis- sion-critical and delay-sensitive s ervices with high pr ior- ity, denote d by Bhig, and other bursts are with low priority,
J.-R. YANG, H.-A. YE Copyright © 2013 SciRes. CN denoted by Blow. Their offered loads are ρ1 and ρ2 respec- tively, and ρ = ρ1 + ρ2. Moreover, the probabilities of channel usage of Bhig and Blow are denoted by u1 and u2, and u = u1 + u2. Further, define λ1 = c1·λ and λ2 = c2·λ, where c1 = ρ1/ρ and c2 = ρ2/ρ are the load ratios of Bhig and Blow in networks. Then, owing to c1 + c2 = 1, the probabilities of channel usage in two-class system are written as and Next, the basics of delay preemption based priority (DPP) are shown in Figure 1, where b is the FDLs length and r is blocking length. Apparently, b should be larger than r to avoid burst congestion in buffer. According to [13], the expectation of r can be presented as where is the mean of Lb, and is its variance. Because Lb is fixed in this paper, namely , it means , and E[r] ≈ Lb/2. Besides, based the result in [8], we design b = Lb. Thus, E[r] = b/2. Furthermore, in Figure 1(a), we see a chann el conten- tion occurs between the high priority burst Bhig, i and low priority burst Blow, j. Under FIFO rule (first in first out), Blow, j cuts through the channel directly. In this case, if the FDL is in the idle/free state, the blocked burst Bhig, i can be buffered and preempt the channel b − r + Lb for itself in advance. Otherwise, Bhig, i would be simply dropped and retransmitted. Hence, for high priority, its loss prob- ability PD, 1 can be written as Figure 1. Principles of delay preemption based priority, (a) blocking of high priority burst; (b) blocking of low priority bursts. ,1 1 1 Pr.{ } D FDL Pcchannel busybuffer busy c uP = = ⋅ (2) where PFDL = P1, FDL + P2, FDL represents the probability of buff er usage, P1, FDL and P2, FDL are the probabilities of buffer usage from Bhig and Blow respectively. Based on [14], the idle probability within the inter-arrival time t can be represented as e−λt. Then, and . In other hand, see Figure 1(b), only the right to be buffered is given to low priority. That means, though it has been delayed b in FDLs, Blow, j would be discarded if a burst arrived within the void b-r. In addition, because of no priority to enter the buffer, an extra burst loss for Blow can be brought when the buffer is idle but pre-reserved by high priority bursts. Therefore, the burst loss probability of low priority can be calcu- lated as ,2 2 1 21 121 1,2, Pr.{ } Pr.{ } (1 ) [ ()()] D FDL FDL FDL FDL Pcchannelbusy bufferbusy channelbusybuffer freec c uPuPc uccc PP = +⋅ =⋅+− ⋅ =⋅+ −+ (3) where (1 − PFDL) is the free probability of buffer. Be- cause PD = PD, 1 + PD, 2 and c1 + c2 = 1, the total loss probability in DPP will be 11211,1, 12 1,2, [ ()()] [ ()] DFDLFDL FDL FDL FDL Pc uPucccPP uc cPP = ⋅+⋅+−+ =⋅+ + (4) Combine Equations (1) and (4), we ge t 2 1,2,1 2 1,2,1 [() ] [() ]1 FDL FDL DFDL FDL cP Pc PcP Pc ρ ρ ++ =+ ++ (5) Then, with the various load ratios, the blocking per- formance of DPP is investigated from a typical simula- tion scenario used in [12], and b is designed as 80 μs specially. In Figure 2, there are two apparent natures on data loss in DPP. First, compared to the result of sin- gle-class, it is certain that there are the obvious reduc- tions on loss probability existing in all traffic states, es- pecially when c1 is a smaller value. Secondly, we find the value of PD is positive proportional to the variant c1. For instance, when c1 = 0.2 or 0.3, a very low PD, less than 10−3, is obtained in light load (ρ < 0.3). Instead, for c1 = 0.5, the burst loss probability is increased quickly, and reaches 2 × 10−1 at ρ = 0.7, which is almost equal to the result of single-class. Although as the minority of net- works, the load ratio of high priority is general less than 30% [15], we should strongly notice that, being in heavy load, a higher PD is also demonstrated when c1 is a small value (e.g. when c1 = 0.2, PD is equal to 10−2 at ρ = 0.7). In one word, DPP is suboptimal due to the fact a higher loss probability still exists in high traffic states. r FDL length=b L b burst dropped Blow,j Bhig,i preemption Bhig,i t (a) burst r B low,j B hig,i t FDL length=b B low,j dropped L b (b)
J.-R. YANG, H.-A. YE Copyright © 2013 SciRes. CN Figure 2. Total loss of DPP. Based on Equations (2)-(4), we take a further analysis for high and low priority on blocking performance, and a typical value 0.3 is selected for c1. The numerical results in Figure 3 indicate that Blow is the main contributor of the total burst loss probability. And for high priority bursts, two apparent natures on PD, 1 are exhibited in dif- ferent traffic states. In light load, its loss probability is just about 1/10 of PD, 2. But, with the increase of offered load, PD, 1 is soared dramatically and reaches 0.33 PD under the condition ρ = 1.0. From Equation (2), the loss of high priority is mainly dependant on the parameters u and PFDL. Considering the majority nature, we infer that such higher PD, 1 in heavy load is resulted from the over-occupancy of the huge low priority bursts on chan- nel and buffer. 3. Limited Delay Preemption Based Priority According to the above analysis, the proposed DPP scheme cannot guarantee the low-loss requirements of high prior- ity bursts because the buffer is unfairly over-occupied by low priority. To overcome the weakness of DPP, it is ne- cessary to take a limitation on buffer usage of low prior- ity within high traffic states. Therewith, an improved scheme called Limited Delay Preemption Based Priority (LDPP) is proposed. In LDPP, the buffered right for low priority bursts is deprived when offered load reaches the designed threshold ρth. Thereby, given the channel con- tention takes place, the burst with low priority will be discarded, whether the buffer is in the idle state or not. We then get PD, 2 = c2u when ρ > ρth. In addition, owing to P2, FDL = 0, the loss probability of high priority bursts PD, 1 is reduced as (6) Therefore, in LDPP, the total loss will be improved and Equation (5) is substituted by 2 1,2,1 2 1,2,1 1 1,2 1 1,2 [() ] 1 [()] () 1( ) FDL FDLth FDL FDL DFDL th FDL cP Pc cP Pc PcP c cP c ρρρ ρ ρρρ ρ ++ ≤ + ++ =+ > ++ (7) From Equation (7), the performance evaluation of LDPP on blocking is developed and the simulation results are shown in Figures 4 and 5. Compared to DPP, in the range of ρth = 0.3 - 0.7, LDPP obtained a blocking im- provement, at least 20%, under the condition ρ = 1.0. Besides, we find that, the lower threshold ρth is selected, the smaller loss probability is gained (see Figure 4). Whe- reas, considering the loss requirements of Blow and the buffer usage efficiency in light load, the value of load threshold shoul d not be too small. Here, an eclectic value ρth = 0.5 is chosen, and the blocking performance of high and low priority is again investigated. Comparatively, on one hand, the loss prob- ability of Blow in LDPP is not deteriorated in all traffic states though the buffered right has been deprived par- tially. On the other hand, the blocking performance of high priority bursts is improved, and more than 40% re- duction on PD, 1 under the condition ρ = 1.0 is shown in Figure 5. In consequence, the total loss probability PD is Figure 3. Blocking of high priority and low priority in DPP. Figure 4. Total loss of LDPP. Figure 5. Blocking comparison between DPP and LDPP. 0.2 0.4 0.6 0.8 1.0 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Offered load per channel Burst loss probability single class c 1=0.2,c2=0.8 c 1=0.3,c2=0.7 c 1=0.5,c2=0.5 0.2 0.40.6 0.8 1.0 10 -5 10 -4 10 -3 10 -2 10 -1 Offered load per channel Burst loss probability c 1 =0.3, c 2 =0. 7 high priority low priority total loss 0.0 0.2 0.4 0.6 0.8 1.0 10 -4 10 -3 10 -2 10 -1 0.4 0.6 0.8 1.0 0.02 0.04 0.06 Burst loss probability Offered load per channel DPP LDPP( ρ th =0.7) LDPP( ρ th =0.5) LDPP( ρ th =0.3) c 1 =0.3, c 2 =0. 7 0.0 0.2 0.4 0.6 0.8 1.0 10 -5 10 -4 10 -3 10 -2 c 1 =0.3, c 2 =0. 7 ρ th =0. 5 Offered load per channel Burst loss probability high priority(LDPP) high priority(DPP ) low priority (LDPP) low priority (DPP)
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