Lower Bound for Mean Object Transfer Latency in the Narrowband IoT Environment

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1 International Journal of Applied Engineering Research ISS Volume 1, umber 1 (017) pp Lower Bound for Mean Obect Transfer Latency in the arrowband IoT Environment Y. J. Lee Department of Technology Education, Korea ational University of Education, 50 Taesungtapyon-ro, Heungdu-u, Cheongu, Chungbu, South Korea. ORCID: Abstract This paper presents analytical model and algorithm to find the lower bound of mean web obect transfer latency, which is one of important measures of quality of Service (QoS) in the Internet. The proposed mean latency model assumes the multiple pacet losses and the narrowband IoT (Internet of Things) environment including multi-hop wireless networ, where fast retransmission is not possible due to small window. Our model also considers the initial estion window size and the multiple pacet loss in one estion window. Computational experiments show that for a given pacet loss rate, round trip time and initial estion window size mainly affect the mean web obect transfer latency. The model can be applied to determine the web obect size satisfying mean response time that end user requires and select the neighbor node with the least transfer latency in the narrowband IoT environment. Keywords: Web obect latency, TCP estion control, Pacet loss, arrowband IoT ITRODUCTIO The web obect transfer latency is one of many important measures in the Internet since it is main factor to affect endend delay. Web applications mainly mae use of transmission control protocol (TCP), which uses a single stream preserving byte order in the stream by assigning a sequence number to each pacet. When any loss occurs in a certain pacet, the subsequent pacets must wait to be delivered to users until the lost pacet will be retransmitted. This retransmission increases transfer latency. Typically, obect transfer latency is affected by data size and transmission time according to transmission rate of lin as well as by TCP estion control mechanism. The common functions of TCP estion control mechanism are start, estion avoidance, timeout, and fast retransmission [1]. Previous related wors on analytical models of data transfer delay over TCP are as following: Padhye [] considered large amount of data transfer on steady state over TCP. Most of TCP connections for web application, however, are short for small amount of data instead of large one in current Internet environment. Connection setup or -start time dominates the performance of web in this environment. oticing this phenomenon, Cardwell [3] extended the above steady state model but he did not consider delay of TCP after time-out. Jiong [4] enhanced the model of [3] considering -start time after timeout of retransmission. However, since the above models assumed wideband networ, they are not able to be applied to the narrowband IoT environment, which this paper considers. That is why narrowband IoT environment and multi-hop wireless networ do not allow fast retransmission of data due to the very small size of window [5]. Lee [6,7] proposed the web obect latency model for HTTP over TCP, T-TCP, and SCTP in the data networ and dealt with the SCTP handover scheme over mobile Internet [8,9]. However they and other previous wors did not consider the effect of the initial window size and the multiple pacet losses in a single window in the IoT environment. Our model estimates the lower bound (LB) when all the pacet losses occur in the last window during start for the transfer completion. The LB of mean obect transfer latency can be found by using our iterative algorithm based on the pacet loss rate, the initial estion window size, the lin bandwidth, and round trip time (RTT). Our model and algorithm can be used in estimating the mean obect delay and determining the web obect size satisfying end-user s required latency in the narrowband IoT environment and multi-hop wireless networ. The rest of the paper is organized as follows. Section describes modeling for mean web obect transfer latency. Section 3 discusses iterative algorithms and computational experiences for mean web obect transfer latency. Section 4 concludes with future wors. MODELLIG FOR WEB OBJECT TRASFER LATECY In order to simplify the model we assume that sizes of web obects are identical and pacets are transmitted in terms of 3365

2 International Journal of Applied Engineering Research ISS Volume 1, umber 1 (017) pp estion window size unit. Let the size of a web obect to transfer be θ Bytes and sender maximum segment size (SMSS) be Bytes. Then, the number of pacets to transfer for an obect is =θ/. When the probability of a pacet loss is p, the expected number of total pacet losses is α= n p by binomial distribution. Congestion control period for the narrowband networ is composed of the start period and estion avoidance period, because fast retransmit and fast recovery are not possible. Therefore, any pacet loss occurs during either start or estion avoidance period. We can identify where any th (=1,.. a) pacet loss occurs by comparing the maximum number of pacets (A, =1,.. a) to be transferred until the threshold (, =1,,..,a) at which estion avoidance starts, with the expected number of pacets (X : =1,,..,a) to be transmitted before the pacet loss. That is, if X A, pacet is lost during start period, otherwise (X > A ), pacet is lost during estion avoidance period. For the data to be transmitted before th pacet loss, ( = for =1), the expected number of pacets sent (including the lost pacet) until the pacet loss is given by 1- (1- p) X p (1- p) 1 1,,, We first consider the worst case in which the amount of retransmission can increase, even if we consider the multiple losses within one estion window. In this case, the estimation of expected number of pacets sent before the pacet loss (X ) in (1) is fairly distributed over the transmission time. That is, pacet errors are spread over time depending on the data amount to be transferred and the pacet loss. The initial value of estion window (cwnd) (IW) is suggested as, 3, and 4 [1]. Initial start threshold ( 1) is set arbitrarily high ( ) and ( ) are set to FlightSize max(, ),3,.., () Here, FlightSize represents the amount of data that has been sent but not yet cumulatively acnowledged. In our paper, we set FlightSize to cwnd by considering worst case. A (=1,,...,a) is the maximum number of pacets to be sent until. Since 1=, A 1 is also equal to. Thus, X 1 is less than A 1. This means that first pacet loss ( =1) must occur during start. Pacets are transmitted in the manner IW, IW, 4 IW, 8 IW, (IW=,3,4) for =1 and IW 1, IW, IW 4, IW 8, (IW=1) for, respectively. Therefore, A is given by (1) A log log 1 1 IW IW if if Generally, we need n windows in order to completely send the obect. Generally n can be expressed in terms of the transmission data amount (Y) and initial window size (IW). n min q : IW log (1 0 1 Y IW ) q1 Y Because X is sent until th pacet loss, the window number (n ) which includes X is given by n X log (1 ) IW IW,3,4 for IW 1 for 1 Congestion window size (C ) corresponding to the window number (n ) is C n,3,4 1 1 IW for IW IW 1 for The maximum number of pacets sent until n th window is given by n 1 n IW,3,4 for 1 B IW IW ( 1) 0 IW 1 for By considering the initial estion window size (IW) additionally, the number of receiver stalls (m) when the obect contains an infinite number of segments [8] is given by q1 m max{ q : rtt IW 0} (8) rtt log 1 1 log IW Therefore, when the transmission data amount (Y) and the initial estion window size (IW) are given, start time is ST( Y ) ( rtt ) IW( where min( m, n 1) 1) Y rtt min log 1 1, log 1 1 log IW IW Here, μ and rtt represent the lin bandwidth and round trip time between sender and receiver respectively. (4) (3) (5) (6) (7) (9) 3366

3 International Journal of Applied Engineering Research ISS Volume 1, umber 1 (017) pp ow we consider the amount of transmission data (Y), retransmission data (R), and the remaining data for transfer before the next pacet loss ( +1) when multiple pacet losses occur in one window after th pacet loss. From Equation (), (3), and (7), it is clear that X A, X, and X B. Therefore, mean web obect transfer latency when the th pacet loss occurs during start is the sum of start time of Y, transmission time of Y, and retransmission timeout as in (10). Y ST( Y) R (10) to Retransmission timeout (R to) is mostly given by 3/ rtt, which can be adusted according to real environment. At the next step, we compute X +1 in Eq. (1) by using +1. Mean web obect transfer latency when the th pacet loss occurs during estion avoidance is the sum of start time of A, additional (M-1) round trip time, transmission time of X, and retransmission timeout. Here, R to is 3/ rtt and can be adustable. ST X ( A ) ( M 1) rtt R (11) to After α pacet losses are processed in either during start or estion avoidance by using the above mentioned model, data for transferring might be still remained. At this time, the remaining data ( α+1) is greater than 0 and since there is no more pacet loss, timeout (R to) in Equation (10) and (11) is not necessary. We can therefore simply find the transfer latency, LT during start (if α+1 A α+1) or LT during es LT ( α+1 ) and LT ( α+1) are given by LT LT ( ( 1 1 ) ST( ) ST( A 1 1 ) 1 ) ( M 1) rtt 1 if 1 A otherwise 1 (1) After pacet losses, α pacets can be transferred either during start or during estion avoidance without error in the last phase. Thus, the LB of mean web obect transfer latency with the number of pacets, =θ/ (obect size = θ and sender MSS = ) is given by Eq. (18). ST( ) LT ( ) (1 ) LT ( ) (13) ( ) Rto where 0 or 1 ITERATIVE ALGORIMS FOR WEB OBJECT TRASFER LATECY Based on the above model and recent TCP estion control standard (RFC581) [1], we can build an algorithm to estimate the LB of mean latency for web obect transfer as in Figure 1. ALGORIM 1. LB of mean latency for web obect transfer 01: IPUT: p, θ,, rtt, μ 0: OUPUT: 03: BEGI 04. Compute the total number of pacets included in a web obect, =θ/ 05: Compute the expected number of pacet losses, α = np 06. Set 1 =, 1 = A 1 = 07: Set 08: while (1) = 0 and = 0 09: if ( >= 1 or p = 0) 10: begin 11: Compute A +1 using Eq. (3) satisfying +1 1: if α A +1 13: Set 14: else 15: Set 16: end 17: brea; 18: ++; = = + α /μ + ST(α) + α /μ + ST(A +1)+ (M-1) rtt 19: Compute the expected number of pacets sent including the lost pacet until the pacet loss, X = - α + 1; 0: Compute the number of pacets sent until start (A ) by using and (3) 1: if (X A ) : begin 3: Compute the window number (n ) and cwnd (C ) using (5) and (6), respectively 4: Set +1 = max{c /, } by Eq. (11) 5: Set 6: end 7: end while = +ST()+ /μ + 3/ rtt 8: Find the LB of mean latency for web obect transfer ( ) 9: ED Figure 1: Mean web obect transfer latency algorithm for LB We compute the LB of mean web obect transfer 3367

4 International Journal of Applied Engineering Research ISS Volume 1, umber 1 (017) pp latency. Generally, mean web obect size (θ) is nown to be 13.5KB and sender MSS () is 536B for WA. If 1095B, the initial value of cwnd (IW) is set to 4 as an upper bound [1]. First, we compute mean web obect transfer latency by varying the web obect size (θ) when the pacet loss rate (p) is 0.0, 0.01and Round trip time (rtt) is 0.1 second and transmission rate of lin (μ) is 10Mbps. Second, we fix the round trip time (rtt) and the initial estion window (IW) for =1 as 56ms and, respectively. And then, we change the pacet loss rate (p) from 0 to 0.. Figure 3: Mean web obect transfer latency for varying the round trip time (rtt) Finally, we vary the pacet loss rate (p) from 0 to 0. after fixing the transmission rate of lin (μ) and the round trip time (rtt), as 10Mbps and as 0.56sec, respectively. We change the initial window size (IW) from 1 to 4. Figure 4 shows the LB of mean web obect transfer latency in this case. Figure : Mean web obect transfer latency for varying the lin speed (μ) Figure depicts the LB of mean web obect transfer latency when the transmission rate of lin (μ) is 1Mbps and 100Mbps. In particular, we can investigate that there is no much reductions in mean transfer latency although the transmission rate of lin (μ) is increased from 1Mbps to 100Mbps. Third, we fix the transmission rate of lin (μ) and the initial window (IW) as 10Mbps and, respectively. We also vary the pacet loss rate (p) from 0 to 0.. Figure 3 depicts the LB of mean web obect transfer latency when the round trip time (rtt) is 0.1second and 1.5second. As we can see in the figure, mean latency is largely affected by rtt. This is why start time significantly increases when the round trip time is relatively large. The LB when rtt = 0.1s is larger than the LB when rtt is 1s for p 0.6. Figure 4: Mean web obect transfer latency for varying the initial window size (IW) COCLUSIOS In this paper, we present the analytical model and algorithm to find the lower bound (LB) of the mean web obect transfer latency in the narrowband IoT environment and multi-hop wireless networ. LB is the mean latency when all the pacet losses occur in the last one window during start, respectively. Our model iteratively finds the latency based on 3368

5 International Journal of Applied Engineering Research ISS Volume 1, umber 1 (017) pp the pacet loss rate and the number of pacets to be transmitted. It also considers the initial value of estion window and multiple pacet losses in one window. The proposed algorithm can easily find the mean latency when the pacet loss rate, web obect size, SMSS, RTT, and the lin rate are given. Computational experiences show that at given the pacet loss rate, round trip time and initial window size mainly affect the web obect transfer latency. Our algorithm can be applied to determine the web obect size satisfying end user s target response time and selecting the neighbor node with the least transfer delay in the narrowband IoT environment. Our wor assumed single user and dealt with extreme pacet loss cases- Lower Bound in order to simplify the model. Future wors include more accurate model considering the probability distribution of burst errors in multiple user environment. REFERECES [1] Allman, M., Paxson, V., and Blanton, E., 009, TCP estion control, RFC-581. [] Padhye, J., Firoiu, V., Towsley, D., and Kurose, J., 000, Modeling TCP reno performance: A simple model and its empirical validation, ACM Transactions on etworing, 8(), pp [3] Cardwell,, Savage, S., and Anderson, Y., 000, Modeling TCP latency,, Proc. IEEE Infocom Conference, pp [4] Jiong, Z., Shu-ing, Z., and Qi-gang, 00, An adapted full model for TCP latency, Proc. IEEE TECO Conference, pp [5] Oliveria, D., and Braun, R., 005, A dynamic adative acnowledgement strategy for TCP over multihop wireless networs, Proc. IEEE IFOCOM Conference, pp [6] Lee, Y., and Atiquzzaman, M., 009, Mean waiting delay for web obect transfer in wireless environment, Proc. IEEE International Conference on Communications, pp [7] Lee, Y., 015, ovel quality of service measure for web transaction in multiple user access environments, International Journal of Applied Engineering Research, 10(16), pp [8] Lee, Y., 016, Some considerations for SCTP handover scheme in mobile networ, International Journal of Applied Engineering Research, 11(11), pp [9] Lee, Y., 016, Location management agent for SCTP handover in mobile networ, International Journal of Applied Engineering Research, 11(11), pp