Modeling and Analysis of Resequencing Delay in Selective Repeat Automatic Repeat Request Jun Li ∗ , Yiqiang Q. Zhao † ∗ Communications Research Centre (CRC) 3701 Carling Ave. Ottawa, Ontario, K2H 8S2 Canada Email: jun.li@crc.gc.ca † School of Mathematics and Statistics Carleton University, Ottawa, Ontario, K1S 5B6 Canada Email: zhao@math.carleton.ca Abstract—In selective repeat automatic repeat request (SR- ARQ) used by a transmitter-receiver pair, data packets correctly received by the receiver need to be delivered to its upper-layer protocol in the same order as they arrived at the transmitter from its upper-layer protocol. In this paper, we propose a novel discrete-time priority queueing network to model SR-ARQ, and study the performance of the resequencing buffer in terms of the mean packet resequencing delay when packets arrive to the network according to a Bernoulli process. Based on the stationary probability distribution of an embedded Markov chain, we derive an explicit expression for the mean packet resequencing delay. Numerical and simulation results of the mean resequencing delay are presented and some performance trends are discussed. This paper presents an analytic framework for accurately computing the mean packet resequencing delay caused by packet retrans- mission in data communication networks. The proposed discrete- time priority queueing network model is expected to be used for performance analysis of ARQ protocols with a more general packet arrival process. I. I NTRODUCTION In packet data networks, it often happens that packets (data units transmitted between a transmitter and a receiver), when they arrive at the receiver, are mis-ordered (i.e., in a different order of their arriving at the transmitter from its upper- layer protocol) mainly due to the following two reasons. The transmitter-receiver pair is connected over multiple channels (or routes) and a packet transmitted over one channel, before it arrives at the receiver, experiences a time delay that may be different from that over another channel. Packets can be lost or erroneously received due to the channel noise, in which case they need to be retransmitted to achieve error-free data transmission via a retransmission scheme, such as the selective repeat automatic repeat request protocol (SR-ARQ), which causes packets to arrive out-of-order at the receiver as well. When it is required by a receiver’s application, such as the TCP protocol, that packets have to be delivered to the application in the same order as they arrived at the transmitter from its upper-layer protocol, referred to as in-sequence delivery, the receiver buffers mis-ordered packets in a resequencing buffer, re-sequences them repeatedly, and delivers packets in the order of their arriving at the transmitter. This process is referred to as packet resequencing. The study of packet resequencing is important in the network performance point of view. The reader is referred to [1] for some network implications related to packet resequencing. In the literature, packet resequencing analysis, often in terms of the packet delay and/or the resequencing buffer length, has been conducted based on one of the mis-ordering causes described above. For instance, studies in [1], [2], [3], [4], [5], [6], [7], [8] conducted resequencing analysis by considering packet mis-ordering caused by multi-route transmission (in- cluding parallel processing), while studies in [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19] considered packet mis-ordering caused by retransmission of packets. The study in this paper belongs to the second group. Automatic repeat request (ARQ) corrects erroneously re- ceived packets through retransmission. SR-ARQ, one of these classical ARQ protocols developed, has been widely used in wireless packet data networks (e.g., [20] and [21]) thanks to its higher efficiency. In SR-ARQ, the transmitter sends packets continuously, while the receiver generates either a negative acknowledgement (NACK) or a positive acknowledgement (ACK) for each received packet and sends it over a feedback channel. Once an NACK arrives at the transmitter, the trans- mitter retransmits the negatively acknowledged packet without re-sending the transmitted packets following it. To preserve the original order of packets arriving at the transmitter from its upper-layer protocol, a resequencing buffer is provided at the receiver to store the mis-ordered packets (i.e., correctly received packets that could not be delivered to a receiver’s application). There are several studies on packet resequencing for SR- ARQ in the literature. In [15] and [18], the resequencing delay and the length of the resequencing buffer were investigated for channels with time-invariant error rates under a heavy traffic condition (i.e., the transmitter has an infinite supply of packets to transmit). With the same traffic condition, an approximated mean resequencing delay of a packet was obtained for an on- off Markov channel model in [11]. In [9] and [10], the global delay experienced by a packet, or the sum of the resequencing delay (i.e., the delay portion of packet in the resequencing buffer among the overall packet delay), transmission delay and queueing delay of the packet, was investigated under a more general traffic assumption (e.g., the Bernoulli process). In summary, analysis of the resequencing delay has only been 792 JOURNAL OF NETWORKS, VOL. 5, NO. 7, JULY 2010 © 2010 ACADEMY PUBLISHER doi:10.4304/jnw.5.7.792-799