Multicasting vs. Unicasting in Mobile Communication Systems Janne Aaltonen
Jouni Karvo
Nokia Ventures Organisation P.O.Box 4, 20251 TURKU, FINLAND
Helsinki University of Technology P.O.Box 3000, 02015 HUT, FINLAND
[email protected]
[email protected]
ABSTRACT We evaluate the multicasting gain over unicast in the cellular networks, where cells are engineered for a specific target call blocking probability. Our approach is Monte-Carlo simulation of dynamic multicast connections, and the traditional Engset model for the unicast traffic. We predict the gain given by multicasting by using earlier studied traffic patterns, and conclude that intervention of the network operator is needed to secure a significant multicasting gain.
Categories and Subject Descriptors C.4 [PERFORMANCE OF SYSTEMS]: Performance attributes; C.2.3 [COMPUTER-COMMUNICATION NETWORKS]: Network Operations—Public networks; C.2.m [COMPUTERCOMMUNICATION NETWORKS]: Miscellaneous
General Terms Performance
Keywords Multicast, mobile networks, dimensioning, blocking
1.
INTRODUCTION
Delivering content to many people at the same time is an effective way to utilize network resources. One way to implement a one-to-many content delivery system is usage of broadcast and multicast technologies. The radio spectrum is a rare resource and is typically considered as the bottleneck in communication systems. The benefits of multicast and broadcast on the air interface is that many users can receive the same data on a common channel, thus not clogging up the air interface with multiple transmissions of the same data. In order to improve efficiency of the mobile radio link, 3GPP (3 Generation Partnership Program) started in 2001 a specification effort to enable support for one to many services. This service was named Multimedia Broadcast/Multicast Service (MBMS).
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Samuli Aalto Helsinki University of Technology P.O.Box 3000, 02015 HUT, FINLAND
[email protected]
The MBMS includes two modes, broadcast and multicast [1]. The broadcast mode is close to traditional television or radio type of concept. The network operator or service provider decides what is offered, where it is offered and when. By keeping the assortment small, the operator can predict of the network’s capability for delivery in a straightforward manner, since the concept relies on the network resource reservation schemes. The multicast mode of MBMS enables user-initiated activation of the multicast service. If the transmission is already on the air end-user joins the ongoing transmission. If the transmission is not in the progress the network starts transmitting the corresponding multicast content [1]. This concept allows end users to request any data, anytime and anywhere and to receive it provided that there is free capacity in the network. This kind of a scenario, where end users are using join and leave- type of messages to access content, leads to multicast trees that change dynamically in time. One of the key parameters when dimensioning a network is the capacity of the network links. In unicast networks the required capacity of the links can be estimated by using Erlang and Engset type models. These models use a circuit switched approach, and the capacity of a link is measured in the amount of calls the link may carry simultaneously. Multicast brings an additional dimension to the estimation since it is possible that two or more end-users are receiving the same data synchronously leading to more efficient use of capacity than in a unicast network. The purpose of the present paper is to estimate this resulting gain given by multicast over unicast in mobile communications networks. To this end, we estimate the number of users a cell can support with a target call blocking probability in both unicast and multicast cases. In the unicast case, we apply the classical result of Engset [7]. For the multicast case, we use Monte-Carlo simulation. For static multicast trees, i.e. trees where users cannot join or leave the tree freely, the models used for unicast can be used (see e.g. [13]). When the users can freely join or leave the connections, the trees are dynamic, and the earlier models do not suffice. Only recently has there been some progress in the analysis of the blocking probability for the dynamic multicast setting. Chan and Geraniotis [6] considered a network with layered multicast traffic, giving closed form expressions for blocking probabilities but relying on approximations and simulation efforts for actual calculations. Karvo et al. [10] showed how to calculate the call blocking probability for any of the multicast channels in a specific link with finite capacity assuming that all the other links have infinite capacity. Here, a basic assumption was that the number of “channels” (multicast contents) is relatively small, such as in a cable-TV network. This work was extended independently by Boussetta and
2.1 Unicast
Belyot [4] and by Nyberg et al. [12] to include unicast traffic. More results have been developed for multicast in the network case; Algorithms for calculating the end-to-end blocking probabilities were presented by Nyberg et al. [12] and Aalto and Virtamo [2]. Simulation techniques were developed by Lassila et al. [11, 9]. The results of these earlier papers are applicable only in such cases where the number of multicast contents is limited, which might not be the case — as an example, consider the practically infinite number of contents in the Internet. In this paper we try to find some insight into the dimensioning problem in dynamic multicast enabled networks with an infinite number of multicast contents implemented in future cellular networks. We present a model that allows the estimation of the maximum number of end-users that can be served by a cell with a fixed capacity under a given call blocking constraint. An important characteristic here is the user preference distribution, i.e. with which probabilities users choose different multicast contents. We studied Zipf type preference distributions with both an infinite number of contents and a truncated distribution for a finite number of contents. This selection is supported by the earlier work of Breslau et al. [5] of Internet content selection. This paper is organised as follows. Section 2 presents the models and algorithms used to calculate and simulate blocking probabilities when using unicast or multicast. Section 3 shows numerical results on the gain given by multicast over unicast in a cellular network. Finally, Section 4 concludes the paper.
2.
For unicast connections, the call blocking probability can be calculated from the well-known Engset formula as the time blocking probability of a system with the user removed (or with users):
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For dimensioning a cell, a target blocking probability and a fixed capacity are used. Then, an inverse of the Engset formula can be calculated numerically, as
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to get the number of users that can be served with the available capacity.
2.2 Multicast Some channels (provided contents) are more popular than the others, and thus have often more simultaneous users. To capture this behaviour, we use a preference distribution. When starting a call, a user selects the channel (content) to access using the preference distribution. We use the Zipf distribution as such, as suggested by the studies of the Internet. The point probabilities are of the form
SYSTEM MODEL AND PARAMETERS
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We consider a single cell in a cellular network. To simplify the analysis, we assume that the interference of the neighbouring cells and other physical and technical constraints can be taken care of by specifying a capacity (in connections) to the cell. The capacity corresponds to the maximum number of unicast connections in the unicast case, and the maximum number of ongoing multicast transmissions in the multicast case. Thus, the mobile cell is reduced to a single transmission link. users resident in the cell. We leave handovers unThere are treated; the main goal of the paper is not in dimensioning but comparison of unicast and multicast, for which purpose a bit coarser model is sufficient. The number of different multicast contents provided, called multicast channels, is denoted by . Each user behaves independently of the other users. The user may either be active of inactive. By “active”, we mean that a user is engaged with an ongoing call. After a call is over, the user is inactive for a period of time. We assume that the times the user is inactive are exponentially distributed with parameter , and the call holding times are exponentially distributed with parameter . Note that for all finite , the time blocking probabilities of the system are insensitive to the call holding time distribution. Let denote the probability that a user is active at any instant of time in a system with no blocking (i.e. the offered user on-time):
In order that multicast give some improvement in efficiency compared to unicast there must be some contents that are clearly more popular than the others. In Zipf type distributions, Equation 2, the parameter controls this phenomenon: the greater , the more popular are the most popular contents (in comparison with the other contents). The work of Breslau et al. [5] indicate that obtains larger values for proxy traces from a homogenous environment than from a diverse user population. Similar result are found in Adamic and Huberman [3]. In our model, the multicast user wakes up from the inactive state with intensity , and then selects channel with probability . After the call, the user returns to the inactive state. The number of channels from which to select is denoted by . The resulting user model is shown in Figure 1. The earlier works (e.g. [10]) calculate (or simulate) the blocking probabilities by convoluting the distributions of channel usages to achieve a link occupancy distribution. Since our target is also , we need to choose a different to simulate cases where approach. In the multicast setting, the preference distribution causes the call blocking probabilities for different channels to be different; if a channel is already carried on the link, there can be no blocking events for this channel. To get a user-wise call blocking probability figure, we need thus to calculate it from the channel-wise call blocking probabilities
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For the sequel, we use the concepts time and call blocking probability. The time blocking probability means the fraction of time the system is in a state where no extra calls can be admitted due to the capacity restrictions. The call blocking probability means the probability that a user’s call attempt fails due to blocking. These two probabilities are closely related but differ, since the user “looks” at the system state only when inactive. We assume that if a call is blocked, the user falls back and starts a new inactive period, i.e. that blocked calls are lost.
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Simulation The call blocking probabilities needed in Equation 3 can be simulated, as described in this section. is the call blocking probability The call blocking probability for a “channel that is never carried on a link”, and equals the time blocking probability of the system with one user removed. The channel-wise call blocking probability for channel in the multicast setting can be simulated as the time blocking probability in a system where one user has been removed from the system and counting only the blocking states where channel is not active. Generation of samples for the system is carried as follows.
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1. The system state can be described by defining the states of the users , where (in most cases ). Thus, a vector of user states is generated by first drawing for each user if they are active, and then drawing a channel number from the preference distribution for the active users.
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Figure 2: Multicast gain with an infinite number of channels. (from top to bottom)
where can be selected so as to make the error insignificantly small. The bound can be explained as follows: Since the probabilities of the preference distribution are monotonically decreasing, the call blocking probabilities must be increasing as a function of channel index . Getting the limit yields the blocking probability . Note that in this case, . This can be thought as a “channel that is never carried on a link”. As for the unicast, the call blocking probability given by Equation 3 can be used for dimensioning purposes:
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3. NUMERICAL RESULTS , called multicast gain, to describe the We use the ratio gain given by multicast over unicast. This corresponds to the factor by which the multicast cell can be bigger than a unicast cell, and should give a rule of thumb for dimensioning purposes. % in We use the target call blocking probability all our calculations and simulations. For the multicast case, we used which was found large enough for the required accuracy. We implemented the algorithms presented in the previous section, and simulated first a scenario where the users can freely select the channel (content) from an infinite number of available contents. Figure 2 shows the multicast gain as a function of the preference distribution parameter . The figure shows that in order to get a significant improvement over unicast, the parameter of the preference distribution must be significantly higher than 1. Note that links with a higher capacity also favour multicast. This is due to the higher number of users supported which increases the likelihood of simultaneous users on multicast channels.
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4. CONCLUSIONS Our results show that for those values of the Zipf distribution parameter that are near to one, multicast does not bring much gain compared to unicast. As increases, however, the advantage comes more and more evident. For example, with a value of two, the advantage is already remarkable. The dependence of the increase of efficiency on indicates that in order to have a significant improvement on the network there has to be a way to influence end users’ content consumption pattern. This can be achieved by offering attractive portals for media consumption or in some cases even offering walled garden type service packets. In addition, the advantage seems to increase, when we consider systems that allow more simultaneous transmissions. The number of simultaneous transmissions in the system can be increased by either adjusting the reserved bandwidth per channel or by introducing a communication system with a larger bandwidth. Provided that the operator can steer the consumption pattern of the end users to popular content and has the capability to offer a large amount of multicast channels, it has an opportunity to increase network efficiency by an order of magnitude.
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We also studied the impact of the number of possible channels available. Figure 3 shows the results for the case where and . As expected, when the number of channels available is smaller, the gain for multicast grows. However, the number of channels must be restricted to rather low a value to have a significant improvement. and Figure 4 shows the results for the case where and the number of channels available is finite. The results are similar to the case where . We also studied the effect of varying the active state probability on the multicast gain. Figure 5 shows the results, normalised to . When the average user activity varies between (36 s during the peak hour) to (6 min during the peak hour), there is no considerable effect. If the user activity rises to very high values, part of the multicast gain is lost. This loss is higher with larger values of . The natural explanation to this phenomenon is that for the values of near 1, the number of users supported by the cell is smaller and thus the likelihood of simultaneous users of a multicast channel is again smaller.
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5. ACKNOWLEDGEMENTS We thank Esa Hyyti¨a for his algorithm for generating random variates for truncated Zipf distributions.
6. REFERENCES [1] 3GPP Technical Specification Group Services and System Aspects. Multimedia broadcast/multicast service, stage 1 (release 5), Dec. 2001. 22.146, v. 5.1.0. [2] S. Aalto and J. Virtamo. Combinatorial algorithm for calculating blocking probabilities in multicast networks. In Proc. 15th Nordic Teletraffic Seminar, NTS-15, pages 23–34, Lund, Sweden, Aug. 2000. [3] L. A. Adamic and B. A. Huberman. The nature of markets in the World Wide Web. Quarterly Journal of Electronic Commerce, 1(1):5–12, 2000. [4] K. Boussetta and A.-L. Belyot. Multirate resource sharing for unicast and multicast connections. In D. H. K. Tsang and
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P. J. K¨uhn, editors, Proceedings of Broadband Communications’99, pages 561–570, Hong Kong, Nov. 1999. L. Breslau, P. Cao, L. Fan, G. Phillips, and S. Shenker. Web caching and Zipf-like distributions: Evidence and implications. In Proc. INFOCOM’99, volume 1, pages 126–134, New York, USA, Mar. 1999. W. C. Chan and E. Geraniotis. Tradeoff between blocking and dropping in multicasting networks. In ICC ’96 Conference Record, volume 2, pages 1030–1034, June 1996. T. Engset. Die Wahrscheinlichkeitsrechnung zur Bestimmung der W¨ahleranzahl in automatischen Fernsprech¨amtern. Elektrotechnische Zeitschrift, 39(31):304–306, Aug. 1918. W. H¨ormann and G. Derflinger. Rejection-inversion to generate variates from monotone discrete distributions. ACM Transactions on Modeling and Computer Simulation, 6(3):169–184, July 1996. J. Karvo. Efficient simulation of blocking probabilities for multi-layer multicast streams. In E. Gregori, M. Conti, A. T. Campbell, G. Omidyar, and M. Zukerman, editors, Proc.
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IFIP Networking 2002, volume 2345 of Lecture Notes in Computer Science (LNCS), pages 1020–1031, Pisa, Italy, May 2002. J. Karvo, J. Virtamo, S. Aalto, and O. Martikainen. Blocking of dynamic multicast connections in a single link. In Proc. of International Broadband Communications Conference, Future of Telecommunications, pages 473–483, Stuttgart, Germany, Apr. 1998. P. Lassila, J. Karvo, and J. Virtamo. Efficient importance sampling for Monte Carlo simulation of multicast networks. In Proc. INFOCOM’01, pages 432–439, Anchorage, Alaska, Apr. 2001. E. Nyberg, J. Virtamo, and S. Aalto. An exact algorithm for calculating blocking probabilities in multicast networks. In G. Pujolle, H. Perros, S. Fdida, U. K¨orner, and I. Stavrakakis, editors, Networking 2000, pages 275–286, Paris, France, May 2000. K. W. Ross. Multiservice Loss Models for Broadband Telecommunication Networks. Springer Verlag, London, 1995.
