Packet Queueing Delay in Resilient Packet Ring Network Nodes

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SHI Guowei (史国炜) et al:Packet Queueing Delay in Resilient Packet Ring Network Nodes 407 RPR protocol defines two types of transit queueing models for network nodes: single-queue (SQ) and dual-queue (DQ). Accordingly, an RPR node may have two kinds of data path structures, as shown in Figs. 2 and 3. The difference between the two data path structures is in the number of transit buffers. The transit buffer (TB) is used exclusively to avoid collisions between transmit and transit packets. The frame-header checker determines the reception and transit conditions for the upstream packets. The arbiter schedules the access of transmit and transit packets to the outgoing link. Fig. 2 Data path structure of a single-queue node Fig. 3 Data path structure of a dual-queue node An RPR network supports client traffic with three priority classes: Class A, Class B, and Class C. In the transmit direction, Class A traffic has higher precedence than Class B which in turn has higher precedence than Class C traffic. According to the priority, the client traffic is inserted into three transmit buffers, which are named Tx-A, Tx-B, and Tx-C, respectively. In the SQ mode, the node places all transit traffic into a primary transit queue (PTQ). In the DQ mode, the node puts Class A transit traffic into a higher priority PTQ, and puts Class B and Class C transit traffic into a lower priority secondary transit queue (STQ). Neither mode supports preemption of either transit or ingress packets. The RPR protocol defines the bandwidth allocation and packet scheduling mechanisms. As shown in Figs. 2 and 3, based on the RPR scheduling mechanism, if we assume that the control packets are negligible in amount and the capacity of all buffers is infinite, the arbiter can schedule packets simply according to the following priority order (from the highest to the lowest): ● Dual-queue ① Packets from PTQ, ② Packets from Tx-A, ③ Packets from Tx-B, ④ Packets from Tx-C, ⑤ Packets from STQ. ● Single-queue ① Packets from PTQ, ② Packets from Tx-A, ③ Packets from Tx-B, ④ Packets from Tx-C. 2 Mathematic Analysis of Queueing Delay Assume that traffic arrival times and service times are independent, that the arrival processes at each transmit and transit buffer are of Poisson distribution, and that all nodes have the same packet-length distribution. Then the traffic queueing model of the RPR data path can be regarded as a non-preemptive priority M/G/1 queueing system, based on the standard queueing theory [7] . In the following, we develop an equation for the average delay for each priority class. The following symbols are used in this paper: Wk is average queueing delay for priority k; λk is average arrival rate for priority k; X k is the first moment of service time for priority 2 k; X k is the second moment of service time for priority k; ρk is the system utilization for priority k; R is mean residual service time. The queueing delay is the time span between the time when the packet is assigned to a queue for transmission and the time when it starts to be transmitted. According to Little’s theorem and the Pollaczek- Khintchine (P-K) formula [8] , the queueing delay for the highest priority traffic is R W1 = (1) 1− ρ where the residual service time R is expressed as 1 n 2 R = ∑ λiX i (2) 2 i= 1 1
408 Tsinghua Science and Technology, August 2004, 9(4): 406–409 For the second priority class, the queueing delay W2 has a similar expression as W1 except that an additional queueing delay has to be counted due to higher priority customers arriving while a lower priority customer is waiting in the queue. W2 is obtained, R+ ρ1W1 W2 = (3) 1−ρ−ρ 1 2 The derivation is similar for all priority classes (k>1), and the formula for the waiting time in the scheduling buffer is R Wk= , k > 1 1−ρ −L−ρ 1−ρ −L−ρ ( )( ) 1 k−1 1 k (4) Suppose that all nodes have the same transmission pattern. The average number of transit buffers traversed by each packet is then obtained, α N −1 = ∑ q ( j−1) j= 2 j (5) where N is the number of the nodes on the ring, and qj is the probability of node i transmitting packets to its jth neighbor node. Assume that traffic of all priorities has the same arrival rate in the transmit buffer. The relationship between the traffic arrival rates in the transit buffer and in the transmit buffer is [9] λTB = αλTx (6) We assume that all packets have the same service time X . The relationship between the system utilization and the arrival rate for each priority class in a node is then ρ1 = αρA (7) For a DQ ring, we identify five priority traffic classes as shown in Fig. 3. Using Eqs. (6) and (7), the system utilization of each priority class can be expressed as: ρ1 = αρA (8) ρ = ρ (9) 2 A 3 = B ρ ρ 4 C 5 ( B C) (10) ρ = ρ (11) ρ = α ρ + ρ (12) From Eqs. (1), (3), and (8)-(12), the queueing delays for each priority class in different buffers are obtained: DQ R WPTQ = (13) 1− αρ A W W DQ B DQ C = = W DQ A = R (1 −αρ ) 1 − 1 + α ρ ( ( ) ) A A R ( ) ( 1− ( 1+ α) ρA) 1− ( ( 1+ α) ρA + ρB) R ( 1− ( ( 1+ α) ρA + ρB) ) 1− ( ( 1+ α) ρA + ρB + ρC) W DQ STQ = ( ) R ( 1− ( ( 1+ α) ρA + ρB + ρC) ) 1 ( 1− ( ( 1+ α) ρA + ( 1+ α)( ρB + ρC) ) ) ( 1 )( ) A B C (14) (15) (16) (17) R = X + α ρ + ρ + ρ (18) For the SQ ring, four priorities are identified as shown in Fig. 2. Similar derivations to those used for the DQ ring can be made. The equations for the system utilization and queueing delay for each traffic class in an SQ ring are obtained: ρ = α ρ + ρ + ρ (19) W SQ A W = W SQ PTQ 1 ( ) A B C ρ2 = ρA (20) ρ3 = ρB (21) ρ4 = ρC (22) R = 1− α ρ + ρ + ρ ( ) A B C R ( ) ( 1− α( ρA + ρB + ρC) ) 1− ( α( ρA + ρB + ρC) + ρA) W SQ C SQ B = R ( 1− ( α( ρA + ρB + ρC) + ρA) ) 1 ( 1− ( α( ρA + ρB + ρC) + ρA + ρB) ) = R ( 1− ( α( ρA + ρB + ρC) + ρA + ρB) ) 1 ( 1− ( α + 1)( ρA + ρB + ρC) ) 3 Simulation Results (23) (24) (25) (26) In the normal operation state, the packets are routed on a minimum hop basis in an RPR network. Therefore, it
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Packet Queueing Delay in Resilient Packet Ring Network Nodes

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