Abstract-Performance analysis of TCP-controUed long file transfers in a WLAN in infrastructure mode is available in the literature with one of the main assumptions being equal window size for all TCP connections. In this paper, we extend the analysis to TCP-controlled long file uploads and downloads with different TCP windows. Our approach is based on the semi  This paper is concerned with infrastructure mode WLANs that use the IEEE 802.11 DCF mechanism. We are interested in analytical models for evaluating the performance of TCP controlled simultaneous uploads and downloads where each connection has arbitrary TCP window size. A detailed analysis of the aggregate TCP download throughput in a WLAN for a single rate Access Point (AP) is given in [1] , where it is assumed that all TCP window sizes are equal. Similarly, aggregate TCP throughput is evaluated for the multi rate case are in [2] and [3]. However, these works also consider only download or upload with constant windows. Here, we consider both uploads and downloads along with different TCP windows. We are motivated to study an analytical model for this scenario because of the clear understanding that it gives, and the useful insights that it can provide. Closed-form expressions or numerical calculation procedures are useful because other features and capability can be built upon them. One such application, which we are studying now, is to utilize the results reported here in devising a improved AP-STA association policy. Our approach is to model the number of STAs with ACKs and data packets in their MAC queues as an embedded Dis crete Time Markov Chain (DTMC), embedded at the instants of successful transmission events. We consider a successful transmission from the AP as a reward. This leads to viewing the aggregate TCP throughput in the framework of Renewal Reward theory given in [4] . Our contribution: We provide a simple approach to model the aggregate throughput of long-lived TCP downloads and uploads with arbitrary maximum TCP receive window size in IEEE 802.11 networks. We use the basic model and results presented in [ 1] . We show that numerical results of our analytical model compare well with simulation results. Simu lations indicate that for the upload-download traffic scenario, our numerical evaluation of the analytical expression matches accurately with maximum error of ± 0.76%. This paper is organized as follows: Section II outlines the related literature. In Section III, we state the system model and we discuss the modelling assumptions. In Section N, we develop the throughput analysis. In Section V, we present performance evaluation results. In Section VI, we discuss the results. Finally, the paper concludes in Section VII. The analytical work in this area has considered saturated and unidirectional traffic, i.e, either uplink or downlink; see, for example, [5] , [6] and [7] . All the above papers assume that all the STAs are saturated, in other words they have packets to send to the AP at all time. In contrast, we consider TCP controlled transfers, where the "saturated nodes assumption" does not apply. All the related work that we are aware of assumes homoge neous TCP connections in the sense that the maximum window size is the same for all connections. [1] and [8] propose a model for a single rate AP-STA WLAN, assuming the same maximum size of TCP window for all TCP connections. An extension of this work in [2] considers two rates of association with long file uploads from STAs to a local server; the multirate case is considered in [3] . [9] and [10] present analysis of TCP-controlled uploads and downloads with UDP traffic in a single cell infrastructure WLAN. They assume equal TCP maximum window size for all connections, that TCP receivers use undelayed ACKs, and show that the total TCP throughput is independent of the number of STAs in the system. Also, upload and download transfers obtain equal shares of the total throughput. The letter [11] gives an average value analysis of TCP performance with upload and download traffic. First, the authors provide an expression for the average number of active TCP stations. In [12] , a finite buffer AP with 978-1-4244-9799-7/11/$26.00 ©2011 IEEE TCP traffic in both upload and download direction is analysed with delayed and undelayed ACK cases. [13] provides an analysis for a given number of STAs and maximum TCP receive window size by using the well known p-persistent model proposed in [7] . However, [13] considers only download traffic or upload traffic, not both together. HTTP traffic is analyzed in [14] . A queueing model is proposed to compute the mean session delay in the presence of short-lived TCP flows. The impact of TCP maximum congestion window size on this delay is studied. The analysis also extended to consider the delayed ACK technique. We consider a WLAN which has M STAs associated with an AP as shown in Figure 1 , and all the M STAs are associated at the same rate. We consider only TCP traffic. Mu STAs are "senders" in uploads and Md STAs are "receivers" in downloads. Thus, the AP sends either TCP ACK packets to the Mu uploading STAs or TCP data packets to the Md downloading STAs. The arrows in Figure 1 show the direction of the data packets in the network. There is also feedback traffic consisting of TCP-ACK packets. I. We assume that M is large. We will show later how big M needs to be for our results to be applicable. Let Wd be the cumulative TCP advertised window size of all downloading STAs and Wu the cumulative TCP advertised window size seen by all uploading STAs. Let W = Wu + Wd be the sum of the maximum size of the TCP windows. All the nodes contend for the channel using the DCF mechanism of IEEE 802.11. We assume that there are no link errors. Packets in the medium are lost only due to collisions. Because of the long file transfer scenario, we can assume that TCP sources are operating in Congestion Avoidance. Hence TCP startup transients can be ignored. Further, we assume that all nodes use the RTS-CTS mechanism while sending data packets and use basic access to send ACK packets. As soon as the station receives a data packet, it generates an ACK packet without any delay and it is enqueued at the MAC layer for transmission. We assume that all nodes have sufficiently large buffers, so that packets are not lost due to buffer overflows. Also, TCP timeouts do not occur. The value of RTT is very small, since files are downloaded from a server located on the LAN as shown in Figure 1 . Thus, several TCP connections exist simultaneously and every station including the AP contends for the channel. Since no preference is given to the AP, and it has to serve all STAs, the AP becomes a bottleneck, and it is modelled as being backlogged permanently. The aggregate throughput of the AP is shared among all M stations. The probability that the AP sends a TCP data packet to a downloading STA is Pd, which is equal to the ratio of the 1 We recall that every TCP receiver advertises a maximum window size. In the absence of packet loss, a TCP sender's window will grow up to this advertised window cumulative advertised window for downloading connections (which we refer to as the "cumulative download window" henceforth), to the sum of the cumulative download and upload windows. Similarly, the probability that the AP sends a TCP ACK packet to an uploading STA is Pu which is, again, the ratio of the cumulative upload window, to the sum of the cumulative download and upload windows. i.e., Pd = �, an Pu = w' Figure 2 shows one possible sample path of the events on the wireless channel in the WLAN. The random epochs Gj indicate the end of the lh successful transmission from either the AP or one of the stations. We observe that most STAs have empty MAC queues, because, in order for many STAs to have TCP-ACK packets or TCP data packets, the AP must have had a long run of successes -and this is unlikely because no special preference is given to the AP. So, when the AP succeeds in transmitting, the packet is likely to be for a STA with an empty MAC queue. Let Sj be the number of STAs with nonempty MAC queues: If the STA is downloading, it has an ACK packet to send, or if it is uploading, then it has a TCP data packet to be sent. If there are n nonempty STAs and a nonempty AP, each nonempty WLAN entity attempts to transmit with probability i3n + 1, where i3n + 1 is the channel access probability under saturation with (n + 1) WLAN entities as in [6] . So Sj evolves as a DTMC over the epochs Gj. This allows us to consider (S j ) G j) as a Markov Renewal Sequence, and S ( t) as a semi-Markov process. We have the DTMC which is shown in Figure 3 ; transition probabilities are indicated as well. By inspection, we can say that the DTMC is irreducible. The Detailed Balanced Equation holds for a properly chosen set of eqUilibrium probabilities. The Detailed Balanced Equation (DBE) is 476 lI(n+ 1) (n+ 1)/(n+2) Fig. 3 . Embedded Markov chain formed by the AP and n stations associated to the AP at the same data rate. The state transition occurs at the end of successful TCP data or TCP-ACK packet transmissions from the contending nodes. 1 (n + 1) 7l" n (n + 1) = 7l" n + l (n + 2) Here, 7l" n is the stationary distribution of the DTMC. From the set of equations given in (1) and L� =o 7l" n = 1, the stationary distribution is 1 1 7l" n = (n + 1) (n!) * (2e) Let X be the sojourn time in a state (Sj). Conditioning on various events (idle slot, collision or successful transmission) that can happen in the next time slot, the following expression for the mean cycle length can be written EnX = Pidle (8 + EnX ) + (PsApTsAP) + Pe (Te + EnX) + (PsSTATsSTA) In the above expression (3), Pidle is the probability of the slot being idle, PsAP is the probability that the AP wins the contention and transmits the data packet or TCP-ACK packet,
REF considers the single rate case, but allows simultaneous TCP uploads and downloads with arbitrary maximum window sizes.
Aggregate AP throughputs for long file transfers in a WLAN controlled by inhomogeneous TCP connections
2011 International Conference on Communications and Signal Processing
2011 International Conference on Communications and Signal Processing
Computer Science