Analysis of Delayed Reservation Scheme in Server-based QoS Management Network Takeshi Ikenaga Ý, Kenji Kawahara Ý, Tetsuya Takine Þ, and Yuji Oie Ý Ý Dept. of Computer Science and Electronics, Kyushu Institute of Technology / TAO of Japan Þ Dept. of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University Abstract This paper proposes an analytical model for delayed reservation scheme, which can be exactly analyzed. By applying it to a server-based QoS management network, we can obtain the related blocking probability and the waiting time distribution of requests, and discuss its performance by means of numerical results. The numerical results show that the delayed scheme can improve the blocking probability by about two order of magnitude compared with the conventional reservation scheme even when a small acceptable waiting time (e.g. 20% of average flow duration). We can conclude that the delayed reservation scheme can lead to significant improvement in a server-based QoS management network performance. Introduction On the Internet, various kinds of multimedia application have used, such as video-conferencing and Internet telephony. In addition, the traffic volume is increasing explosively with non real-time communication by Web browsing and peer-to-peer style file-sharing (or file-exchange) applications. Thus, the traditional best effort Internet must be changed to support real-time applications which need a QoS guarantee. To provide QoS-aware communication, some architectures such as the Integrated Services (IntServ) [] [2] and the Differentiated Services (DiffServ) [3] [4] [5] have been introduced by working groups of the Internet Engineering Task Force (IETF). Moreover, Bandwidth Broker architecture [6] [7] and COPS (Common Open Policy Service) protocol [8] have been also proposed in the IETF for realizing centralized server-based policy and/or bandwidth management. We focus here on the intra domain (e.g. campus network) QoS management by using centralized QoS server such as Bandwidth Broker or Policy Server that provides a function of end-to-end resource allocation [9]. Conventional resource reservation protocols [0] are immediately rejecting requests, when they are not acceptable because there are no available resources upon their arrivals. Some recent work on deferred reservations [] has introduced mechanisms This work was supported in part by TAO of Japan under the Project Japan Gigabit Network research project (JGN-R40), and a Grant-in Aid for Scientific Research on Priority Areas (2) (409074) of the Ministry of Education, Culture, Sports, Science and Technology, Japan. to reduce the overall blocking probability compared to that with the all-or-nothing reservation approach. The hop-byhop deferral scheme proposed there enforces reservation requests to wait at intermediate routers if there is no available path ahead of them. The requests waiting at the router can be forwarded if any path to their destinations becomes available. Thus, the scheme can not make use of multiple available paths between a source and a destination once the deferral process begins. We have proposed a delayed path reservation scheme for a server-based QoS management network and examined the effectiveness of this scheme through computer simulation [2]. Multiple paths can be utilized efficiently, unlike in the above scheme. In this paper, we propose an analytical model for delayed reservation scheme, which can be exactly analyzed. By applying it to a server-based QoS management network, we can obtain the related blocking probability and the waiting time distribution of requests, and discuss its performance by means of numerical results. From numerical results, we will show that the delayed reservation scheme is very effective in improving the blocking probability in some context of practical interest even if acceptable waiting time is small, say 20% of the average communication time (or service time in the terminology of the queueing system). The rest of this paper is organized as follows. In Section 2, we present a motivation of delayed path reservation scheme and describes its basic approach. In Section 3, we analyze the model. In Section 4, we give some numerical results to show the effectiveness of our scheme, and we conclude in Section 5. 2 Delayed Reservation In this section, we describe the outline of our QoS management scheme and the proposed delayed reservation scheme. 2. Motivation Figure shows a basic model of a server-based QoS management network. The key components of this framework are the user terminal, router, and resource manager (the QoS management server). The QoS management server knows the network topology and manages QoS information such as physical/available bandwidth of links of the whole network.
User Terminal Request Response Server Provisioning Data Flow Resource Management QoS Routing User Terminal Figure. Server-based QoS management model To provide QoS for end-to-end communication, network resources should be reserved according to the QoS requirements. When resources need to be reserved along a path from a sender to a receiver, a resource allocation request is first sent to the QoS management server. But if the network is overloaded, many requests will be rejected. A user who receives a reject message will have three alternatives to choose: Use best-effort communication even if the desired quality of service cannot be expected. (start communication with downgraded QoS) Send the QoS request again after waiting for some duration. (retry manually) Abandon the communication attempt. We are interested here in the first two cases, where requests can wait for a while instead of being immediately rejected. If a user is willing to tolerate an initial setup delay, which is referred to as the acceptable waiting time from now on, we will be able to improve the blocking probability by delaying the path reservation. Then, we will propose a scheme to improve the blocking probability by delaying the path reservation to some extent if there is no available path meeting the requirement when requested. 2.2 Delayed Reservation Scheme Delayed path reservation scheme can be described as follows.. The QoS management server receives a path reservation request from a user and tries to find a route meeting the requested QoS. (a) If a new request is acceptable, the server will accept it and accordingly allocate the network resources. (b) If a new request is not acceptable, it will be stored in the tail of the waiting buffer. If the waiting buffer is already full, the server will reject the request. 2. When a network resource is released because of the termination of a previously accepted communication, the server will examine whether requests waiting in the buffer can be accepted. Request Arrival N Reject (Timeout) Delay c servers Figure 2. Queueing Model Accept 3. When a request has been forced to wait longer than the user s acceptable waiting time, it will be rejected and deleted from a buffer. Therefore, a request can be rejected in two cases when there are no resources available that meet its requirement and there is no space in the waiting buffer, and when the waiting time in the buffer exceeds the acceptable waiting time. 3 Analytical Model In the network, we assume that QoS requests from users arrive at one QoS server according to Poisson process with parameter, and that the distribution of the processing time of one request follows the exponential distribution with parameter. If the server can deal with up to requests simultaneously and it further accommodates Æ requests in the waiting room, we can model the server as ÅÅ Æ queueing system. It is natural for the server to block some request when its waiting time exceeds Ì, so that we should analyze the ÅÅ Æ system with waiting time limits (Figure 2), and derive the waiting time distribution and the blocking probability of requests. Ô Æµ First of all, we will derive the steady state probability,, that the number of requests are in the system when the buffer size is set to Æ. When we take a view of transition of the number of requests in the system, we find that the state when it is or less and that when it is over change alternatively. Furthermore, we can find that the duration of the former state follows i.i.d. and it is independent of Æ, namely, the conditional steady state probability Õ on the duration when the number of requests is or less in the system is also independent of Æ. Thus, we first derive its average duration when Æ. At this time, i.e., in the ÅÅ queueing system, Ô µ ( ) is given as follows. Ô µ Ò Ò Ò Ô µ Ô µ µ () Therefore, we can give the conditional steady state probability Õ as Ô µ Õ Ô µ µ (2) Furthermore, the average duration when the number of requests in the system is becomes, the relation of Ô µ 2
and is given by the following proportional expression, Ô µ Ô µ (3) Here, we define the average duration when the number of requests in the system is over as Ƶ, which is dependent on Æ, so we finally get Ô Æµ as follows. Ô Æµ Ƶ Õ µ (4) From Eq. (4), we should focus on the behavior of the duration when the number of requests is over and derive Ƶ. In the following subsections, we will investigate it in two cases, namely, Æ and Æ. 3. Case when Æ As previously mentioned, the state when the number of requests in the system is or less and that when it is over change alternatively, thus we only focus on the latter state in detail. In this duration, the maximum number Æ of waiting room is set to, so that the number of waiting requests becomes or. Let denote the random variable in terms of the period when the number of waiting requests is and be that when it is. Since we assume the analytical model as ÅÅ Æ system, both variables are independent each other. Thus the Laplace transform of the probability distribution function of the sum of and, µ, can be defined as follows. µ In order to derive µ, we must show all the events occurring in the duration when the number of requests in the system is over. After it becomes, one of following three events will occur:. The service of any one of requests is finished and the number of requests being serviced becomes. 2. New request arrives at the server and the number of requests in the system gets. However, if the waiting time of this request exceeds Ì, the request will be deleted. 3. New request arrives at the server, and then it will be served. Let Ò denote the above event Ò Ò ¾ µ. Moreover, on the condition that any of these events occur, let denote the random variable in terms of the period when the number of waiting requests is and be that when it is. After the beginning of this duration, some request arrives at the server according to Poisson process with parameter, and that the distribution of the processing time of some request out of ones being serviced follows the exponential distribution with parameter. Here, we denote the indicator function of event by µ, the Laplace transform in terms of the event Ò Ò ¾ µ is derived as follows. µ µ ¾ µ ¾µ µ µ Ü Ü Ü Ü (5) Ü Ü Ì µ Ü Ì Ü (6) Ì Ü Ü Ý Ü Ýµ Ü Ý (7) When event occurs, the duration when the number of requests in the system is over ends, and if event ¾ or happens, the duration starts again due to the memoryless property of exponential distribution. Thus, the Laplace transform µ can be expressed by the following equation. µ µ ¾ µ µ µ (8) By using Eq. (8), we can get the average duration when the number of requests in the system is over, µ, as follows. µ ÐÑ µ (9) We define the probability Ô µ Ô µ as, so that the probability that a new arrival request is served immediately is given by µ µ (0) the probability Ô µ that the new arrival request waits for the waiting room is also given by Ô µ ÐÑ µ µ µ () Since the QoS management server rejects the waiting requests when it does not finish to serve any one of requests being serviced until its waiting time gets Ì, the associated probability is defined as Ô µ Ì (2) Furthermore, the probability Ô µ that the new arrival request is immediately blocked is as follows. Ô µ ÐÑ µ µ µ (3) From Eqs. (2) and (3), we can define the blocking probability, È,as È Ô µ Ô µ Ì Ô µ (4) 3
and the probability distribution function Ï Üµ of the waiting time of requests that can be served is derived as follows. Ï Üµ Ô µ Ü µ if ÜÌ È if Ü Ì (5) 3.2 Case when Æ Next, we deal with the case when Æ, namely, ÅÅ queueing system with waiting time limits when. As same in the previous subsection, we will focus on the state that the number of requests in the system is over. Namely, we ignore the state that the number of requests is or less. Therefore, the virtual waiting time of the assumed system is identical to that of the queueing system with waiting time limits Ì on the condition that both service time and vacation time follow the exponential distribution with parameter. This model has been analyzed in [3], so that some performance measures we are interested in are directly given from analytical results obtained in [3]. Let Ï Üµ be the probability distribution function of the virtual waiting time when the limitation Ì is,wegive it as Ï Üµ Ü µý Ü Ýµ Ý (6) From Eq. () in [3], the average duration when the number of requests in the system is over, µ, is given as follows. µ Ï Ì µ (7) where and the probability that some new arrival request is stored in the waiting room is derived by µ µ (8) From Eq. (3) in [3], we can define the blocking probability, È, that the waiting time of requests in the system reaches Ì, as follows. È µ Ï Ì µµ (9) Ï Ì µ Furthermore, from Eq. (4) in [3], the probability distribution function Ï Üµ of the waiting time of served requests is thus derived as follows. Ï Üµ Ï Üµ Ï Ì µ if ÜÌ if Ü Ì (20) N=, /µ=80, c=0 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ρ = =0.2 =0.5 Figure 3. Blocking probability (Æ ) ρ =0.8 ρ =0.6 ρ =0.4 /µ=80, c=0 0 0.2 0.4 0.6 0.8 N= Figure 4. Blocking probability (Æ ) 4 Numerical Results In this section, we will investigate the effectiveness of the delayed path reservation scheme described in Section 2, by showing performances of the blocking probability and waiting time as functions of the number of servers, the offered load µ and the acceptable waiting time Ì. We will first show numerical results in the case that Æ, and then Æ by generally setting the average flow duration to 80 (sec.) and to 0. Furthermore, we change some parameters according to the actual network topology and explain the effectiveness of the scheme. 4. Case when Æ We first show the case when Æ, i.e., if the QoS server can not find any QoS path for the request from some router, only one request can wait in the QoS server. Figure 3 illustrates the impact of the ratio Ì of the acceptable waiting time to the average flow duration on the blocking probability. In this figure, the x-axis indicates the offered load. Compared with the case of, it is found that the blocking probability improves by about 50 % when and Ì ¾. However, even if Ì is set to larger value, the blocking probability keeps almost same value. To investigate the sensitivity of this limitation, the blocking 4
Waiting Time 80 60 40 20 00 80 60 40 20 maximum 99 percentile 98 percentile N=, /µ=80, c=0, ρ =0.6 0 0 0.2 0.4 0.6 0.8 Figure 5. Waiting Time (Æ ) Waiting Time 80 60 40 20 00 80 60 40 20 maximum ρ =0.6 ρ =0.7 ρ =0.8 N=, /µ=80, c=0, 98 percentile 0 0 0.2 0.4 0.6 0.8 Figure 6. 98-percentile Waiting Time (Æ ) N=, /µ=80, c=0 = =0.2 e-05 =0.3 =0.4 e-06 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 7. Blocking probability (Æ ) ρ =0.8 ρ =0.6 ρ =0.4 0 0.2 0.4 0.6 0.8 ρ /µ=80, c=0 N= Figure 8. Blocking probability (Æ ) probability as a function of Ì is also shown in Figure 4. We can see from this figure that it does not improve further when Ì ¾ independently of. Figure 5 shows maximum, 99- and 98-percentile waiting times as a function of the ratio Ì. Here, the maximum waiting time equals Ì and is in proportion to Ì becomes is fixed to 80. However, although both 99- and 98-percentile waiting times becomes larger as Ì increases, they keep almost the same value when it exceeds about 0.25. For example, if Ì, 99- and 98-percentile waiting times become about 30% and 5% of the maximum one, respectively. The impact of the offered load on the 98- percentile waiting time is also shown in Figure 6, and it is found that even if is set to i.e., relatively high, the 98- percentile waiting time becomes quite smaller than a half of maximum one. Thus when Æ, we can conclude that performance does not improve when the acceptable waiting time Ì is set to 25% of the average flow duration or larger due to the strict limitation of the buffer size. 4.2 Case when Æ Next we will deal with the case when the buffer size of waiting requests Æ. Figure 7 shows the impact of Ì on the blocking probability, as a function of the offered load. We can see from this figure that the blocking probability improves by about one order of magnitude when and Ì. As same in the previous subsection, the blocking probability as a function of Ì is also shown in Figure 8. Unlike in the case of Æ, the blocking probability is monotonously decreasing as Ì. However, as shown in Figure 9, both 99- and 95-percentile waiting times are monotonously increasing as Ì. It is found that 99- and 95-percentile waiting times are about 75% and 30% of the maximum one, respectively, over a wide range of Ì. 4.3 Impact of We will examine the impact of parameter. It can be thought that is the maximum number of paths which can be set up by QoS management server. In an actual network, the value of is determined by the number of routers, the number of links, link bandwidth, request bandwidth, network topology, etc. Figure 0 shows the impact of on the blocking probability, as a function of the offered load. We can see from this figure, large results in low È when Ì and are fixed. Figure represents È as a function of. For Æ, the delayed reservation scheme improves È by about 40% compared with the over a wide range of when. In contrast, the case when Æ, large leads to large improvement on È compared with the. Therefore, in a network where is rela- 5
Waiting Time 80 60 40 20 00 80 60 40 20 maximum 99 percentile 95 percentile N=, /µ=80, c=0, ρ =0.6 0 0 0.2 0.4 0.6 0.8 Figure 9. Waiting Time (Æ ) c=0 c=20 c=30 c=40 N=, /µ=80, =0.2 e-05 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 0. Blocking probability (Æ Ì ¾) tively large, the delayed reservation scheme can improve the blocking probability even when a small acceptable waiting time (Ì ) are assumed. 5 Conclusions In this paper, we propose an analytical model for delayed reservation scheme, which can be exactly analyzed. Conventional resource reservation protocols are immediately rejecting requests, when they are not acceptable because there are no available resources upon their arrivals. We focus on a way to improve the blocking probability by delaying the path reservation to some extent if a user is willing to tolerate an initial setup delay, which we refer to as the acceptable waiting time. We then evaluate the performance of this scheme by focusing on the blocking probability and the waiting time, by applying our analytical model to a serverbased QoS management network. From numerical results, the delayed scheme can improve the blocking probability by about two order of magnitude compared with the conventional reservation scheme even when a small acceptable waiting time (e.g. 20% of average flow duration,, ). We can conclude that the delayed reservation scheme can lead to significant improvement in a server-based QoS management network performance. ρ e-05 /µ=80, =0.2, ρ =0.6 N= N= e-06 0 5 0 5 20 25 30 35 40 45 50 c Figure. Waiting Time ( Ì ¾ ) References [] J. Wroclawski, Specification of the Controlled Load Quality of Service, RFC 22, Sep. 997. [2] S. Shenker, C. Partridge, and R. Guérin, Specification of Guaranteed Quality of Service, RFC 222, Sep. 997. [3] S. Blake, et al., An Architecture for Differentiated Services, RFC 2475, Dec. 998. [4] J. Heinanen, F. Baker, W. Weiss, and J. Wroclawski, Assured Forwarding PHB Group, RFC 2597, Jun. 999. [5] A. Charny, et al., An Expedited Forwarding PHB (Per-Hop Behavior), RFC 3246, Mar. 2002. [6] K. Nichols, V. Jacobson, and L. Zhang, A Two-bit Differentiated Services Architecture for the Internet, RFC 2638, Jul. 999. [7] H. Manzoor and M. Yoshida, ENICOM S BAND- WIDTH BROKER, Proc. IEEE SAINT200, pp.23 220, Jan. 200. [8] D. Durham, Ed., et al., The COPS (Common Open Policy Service) Protocol, RFC 2748, Jan. 2000. [9] G. Apostolopoulos, et al., Server Based QoS Routing, Proc. IEEE GLOBECOM 99, pp.762 768, Dec. 999. [0] R. Braden, L. Zhang, S. Berson, S. Herzog and S. Jamin, Resource ReSerVation Protocol (RSVP) Version Functional Specification, RFC 2205, Sep. 997. [] S. Norden and J. Turner, DRES: Network Resource Management using Deferred Reservations, Proc. IEEE GLOBECOM 0, pp.2299 2303, Nov. 200. [2] T. Ikenaga, Y. Isozaki, Y. Hori, and Y. Oie, Performance Evaluation of Delayed Reservation Schemes in Server-based QoS Management, to appear in Proc. IEEE GLOBECOM 2002, Nov. 2002. [3] T. Takine and T. Hasegawa, A Note on Å Vacation Systems with Waiting Time Limits, Advances in Applied Probability, vol.22, no.2, pp.53 58, 990. 6