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1 On-line Trac Contract Renegotiation for Aggregated Trac R. Andreassen and M. Stoer a a Telenor AS, P.O.Box 83, 2007 Kjeller, Norway. fragnar.andreassen, mechthild.stoerg@fou.telenor.no Consider an ATM service, which is d by the contracted peak rate, but where it is possible to renegotiate the peak rate against paying a small renegotation. Such a service represents a more exible economic resource sharing than the current practice of xed capacities. We present an on-line algorithm for renegotiating the peak rate that trades o peak rate s, renegotiation s and long-term. We compare the performance of the algorithm in terms of and with the optimal strategy employing full knowledge of the future trac, and with the constant bit rate strategy. Experiments in a simulation and in an experimental environment with aggregated TCP/IP trac over an ATM link show that the on-line algorithm considerably reduces the gap between the optimal and the constant bit rate strategy. 1. Introduction A renegotiated guaranteed service with the possibility of dynamic peak rate changes could in the future be oered in order to e.g., make leased line services more attractive to customers with long-term trac uctuations, such as managers of corporate and university networks. Compared to xed capacity leased lines, the service has a potential for improved total utility of the link resource, while still giving customers possibilities for cost/quality tradeos through choice of service renegotiation strategy. The task of making these cost/quality tradeos by dynamically balancing communication s, renegotiation s and costs is however non-trivial, and would be more or less impossible to perform by a human operator. Instead, this functionality may be built into an intelligent software agent, acting on behalf of the ATM-link operator or corporate network manager. The aim of this paper is to investigate and evaluate an algorithm for renegotiated service deployment that may be built into such agents. Andreassen et al. [1] study a related problem, arising when the peak rate is xed but the customer can (re-)negotiate a tari depending on the mean rate. Literature on renegotiation has up to now mainly been concerned with video applications. Zegura et al. [2] survey optimal and approximative algorithms for nding renegotiation schedules for video trac traces. Almesberger et al. [3] demonstrate that video conferencing employing renegotiated constant bit rate service (RCBR) over ATM can have acceptable quality. The peak rates were renegotiated manually as picture content shifted This work was supported in part by the European Union under ACTS Project CA$hMAN (AC-039)

2 between \moving" and \slide show". Grossglauser et al. [4] argue that RCBR leads to better shared network resources between connections with variations in slow time-scales. Renegotiation for playback-video and for a link with (aggregated) TCP/IP applications diers in one important aspect: future demand is not known. This necessitates the search for and analysis of eective on-line algorithms for taking renegotiation decisions. We make the following assumptions inuencing the design and analysis of the on-line algorithm. There is no knowledge about trac characteristics and throughput preferences of the single connections carried through the link. There is no knowledge of oered trac, s and buer backlogs, because trac is aggregated, and adaptive trac backs o when encountering a bottleneck. Future capacity requirements are not known. Past sent trac, aggregated over certain intervals, is assumed to be known. Short-term s are unimportant. The customer (leasing a line, e.g.) is mainly interested in the reduction of long-term, experienced by connections through the link, when link capacity is restricted. The probability for refusal of a trac contract renegotiation is negligible. In practical applications, a request for higher peak rate may be refused, but one may assume the network to be dimensioned such that refusals happen rarely. We did not investigate the role of refusal probability on the design of renegotiation schedules. The for renegotiating the capacity is non-negligible, and the s for communication are proportional to the capacity (peak rate). This paper proceeds by presenting the exact meaning of that will be used in the analysis, and establishing the related optimisation problem. We then propose an on-line algorithm. The results from the on-line algorithm are compared with the results from the optimal algorithm and with results from the \simple strategy" of keeping the peak rate xed. The algorithms are evaluated in two scenarios: rst, where values are computed by simulation, and second, where s are measured from reproducible experiment trac. 2. Delay and cost For a given communication over a given type of service one may formulate the economic objective of obtaining the combined minimum of communication cost and cost. Delay is modelled by the uid ow concept: oered trac is seen as a constant ow inside the polling intervals (since nothing is known about the individual trac sources). The backlog buer is virtual, but has a piecewise constant service rate, namely the contracted capacity. An example workload diagram may look like in Figure 1. The volume is the area between the service rate (dotted line) and the oered trac volume (solid line) whenever the service rate is lower than the oered trac. The service rate in the gure is constant inside [t 0, t 1 ] and is renegotiated toalower value at t 1. For each interval of constant service rate, there will be associated a related to the capacity, a related to the capacity renegotiation, and a cost (or rather a penalty) related to the accumulated volume in the period. We chose to penalise the

3 volume V 0 V 1 t 0 t 1 time Figure 1. Volume/ diagram for link model volume instead of the maximum, because this is a better measure for what a number of adaptive trac sources through a congested ATM-link experience over time. For a connection lasting a number of n intervals partitioned at the instants t 0, t 1,..., t n,1, the complete cost is expressed as C = n,1 X i=0 h l (t l+1, t l )+nw r + w d n,1 X i=0 V i : (1) The constant w r denotes the network's for renegotiations, and the constant w d expresses the user's preference for small s. The degrees of freedom in optimising the above objective function lie in the choice of renegotiation instants and peak rates. 3. Optimal renegotiation strategy In order to evaluate how well an on-line algorithm minimises the cost, an algorithm for computing optimal renegotiation schedules was implemented. The optimal algorithm assumes complete knowledge of future trac oered to the link. The algorithm is based on the same idea as a dynamic programming algorithm developed by Grossglauser et al. [4] for renegotiated CBR service. In their setting the cost function C = n,1 X i=0 h l (t l+1, t l )+nw r is to be minimised under the condition that buer occupancy never exceeds a given bound. In our setting, the cost function (1) is to be minimised without conditions on buer occupancies. The algorithm of [4] is easily adapted to the above minimisation problem. It operates with the assumptions that renegotiation decisions can be made only at equidistant time slots, that peak rates can only be chosen from the discretised values f0;; 2;:::;Kg for some bitrate, and that oered trac rates take the same discretised values f0; ; 2;:::g without upper bound.

4 4. Heuristic algorithm for capacity renegotiations An on-line algorithm for capacity renegotiations has to deal with two uncertainties, rst uncertainty about the future trac volumes, and second uncertainty about presently oered trac and s. The only information the algorithm can use are trac observations from the past gathered at xed polling intervals. Note that oered trac is not equal to observed trac, especially when oered trac exceeds the present link peak rate. In order to deal with the unknown future, the on-line algorithm observes the past. If the \cost savings" by awould-be renegotiation to some other peak rate than the present exceeds a certain bound, a renegotiation to this peak rate is proposed. In order to deal with the unknown, the on-line algorithm makes a guess about oered trac. More specically, if the observed trac rate in the last interval is \well below" the present peak rate (i.e. peak-rate, ), then oered trac is assumed to be equal to observed trac. If the observed trac is \near" the present peak rate (i.e. > peak rate, ), oered trac is assumed to be (peak rate + ). The so-called critical region heuristic depends on a parameter c r (renegotiation ), a parameter c d (unit cost), and a discretisation of peak rates. At each polling interval the platform calls the critical region heuristic and passes it the trac rate observed in the last interval. The heuristic will either propose to stay with the present peak rate or propose renegotiation to a peak rate in the set f; 2;:::;Kg. The parameters c r and c d should not be confused with w r and w d of the objective function. In the performance analysis, c r and c d are varied to study the behaviour of the heuristic, whereas w r and w d stay xed. We describe one step of the so-called critical region heuristic. The internal data structure consists of an array of critical regions indexed by the possible peak rates. A critical region for a peak rate consists of a eld started and a eld target time. Starting a critical region means to set started to true and set the target time to a certain time past the present time. Stopping a critical region means setting started to false. As soon as the present time exceeds the target time for a started critical region, a renegotiation to the peak rate associated to the critical region is proposed. One step of the critical region heuristic: If the observed trac rate is > (present peak rate, ), and the critical region belonging to (present peak rate + 2) is not yet started, start it now and set its target time to: present time plus the square root of 2c r =(c d ). The reason behind this setting is that we assume oered trac to be (present peak rate + ) from the start of the critical region and for some time in the future. Under this assumption the cost (c d assumed ) incurred between start time and target time will exceed the cost for one renegotiation. If the observed trac rate is > (present peak rate, ), and the present time exceeds the target time of the critical region belonging to (present peak rate + 2), propose a renegotiation to (present peak rate + 2), stop all critical regions, and exit. If the observed trac rate is (present peak rate, ), stop the critical region belonging to (present peak rate + 2). For all critical regions belonging to peak rates k with k < present peak rate and

5 k (observed trac rate + ) do the following. { If the critical region is not started, start it now and set its target time to present time plus 2c r = (present peak rate, k). The reason for this setting is that the schedule renegotiating to k at start time of the critical region and then renegotiating back again will become cheaper than the schedule waiting until target time, when oered trac rates stay below k between start and target time. { If the present time exceeds the target time of the critical region, propose a renegotiation to k, stop all critical regions, and exit. Stop all critical regions belonging to peak rates k with k < (observed trac rate + ). The workings of the algorithm are illustrated in Figures 2 and 3. The \waiting time" until a renegotiation decision is made, depends on the size of c r and c d. For small c r or large c d values, the algorithm will wait a shorter time. The inuence of smaller or larger c r and c d values on s and is investigated in the next section. rate Renegotiate? Contracted rate rate Renegotiate? Observed rate time δ Contracted rate δ Observed rate time Figure 2. Increasing load Figure 3. Decreasing load 5. Environments for renegotiation strategy evaluation The approach taken for evaluation of the algorithms is to let them work on reproducible trac trace samples. The samples were obtained by making measurements with the CA$hMAN charging management platform on the trac on the ATM link connecting Telenor R&D to its internet service provider. The link speed during measurements was set to an ATM payload rate of 10 Mbit/s. The trac was well below this limit. It is assumed that trac is adaptive, translating communication restraints into communication s. The algorithms were analysed in two environments, by simulation and by experiments Simulation environment In the simulation environment, the backlog buer can be modelled by a leaky bucket, and oered trac can be read directly from original statistics. The simulation

6 environment thus provides for speedy evaluations compared to experiments performed in real time. The optimal renegotiation strategy can only be worked out in a simulation environment, and most comparativeinvestigations are therefore performed by simulations Experimental environment As a validation of operational properties, the on-line algorithm is in addition run in real time in an ATM network fed by computers recreating the original trac trace by TCP/IP trac over ATM. The use of given trac samples allows the computation of backlog volumes aggregated during experiments with the algorithm. The two environments serve to investigate how theoretical results relate to an environment where rate adaptations are not perfect, and where other random eects, such as scheduling s, can be observed. The experiment system consists of a non-adaptive source generating trac as observed from the original unconstrained data transfer, a backlog buer storing information that cannot be immediately sent, and an adaptive source that uses a TCP connection in order to get realistic rate adaptation. Generated trac goes through an ATM network consisting of one link, where actual transmitted data at the ATM level is measured in a charging platform. This platform also controls link rates of the connection to be d, where level and duration of link rates are governed by the renegotiation agent. Time granularity of the agent is approximately ve seconds, i.e., decisions on renegotiations are made with this period. The data source is piecewise constant with the same period as the agent. One important dierence between the experimental environment and the simulations is the nature of rate adaptations. In TCP this adaptation is normally made by probingly increasing the send rate until packet losses occur, whereafter the send rate is reduced before a new increase. By testing the link utilisation using a greedy TCP source, it was experienced that in the range of bitrates used in the experiments, 20% of the capacity consistently remained unavailable for transmission of user data, presumably due to the above rate adaptation mechanism. To obtain correct algorithm performance in the experiments, the observed rates passed to the on-line algorithm were thus increased by a factor 1.25 from the measured value. In the simulation and experiment platforms s were computed dierently. The simulation computes volumes from the statistical trace directly, whereas the experiment platform sums up ( volume) for each packet received. Delay is here the time spent in the software backlog buer. Transfer time over the link was virtually zero. A small test with constant link rates was performed to compare values from the two environments. The test showed that experimentally measured s vary little (when using the same link rate) and that experimental and simulated values conform in the range of non-negligible values. 6. Observations/results Experiments were conducted on several dierent trac trace samples, with dierent c r, c d parameters (controlling step sizes in the critical region heuristic). The largest observed rate in any of the used samples was 5 Mbit/s. The length t of the polling interval was 5.2 seconds with little variation. It was experimented with a peak rate discretisation of = 0.5 Mbit/s. The trac trace samples had been collected during busy hours and morning

7 hours with less trac. Table 1 describes the traces used in the analysis. Table 1 Traces used in the analysis Trace Length (hours) Remark 1 24 working day 2 24 working day 3 1:35 busy hours 4 1 morning hours, little activity We compared the performance of the critical region heuristic with the optimal algorithm and with the strategy of not renegotiating at all. The outputs of the dierent algorithms can be evaluated by two numbers, the, which is dened as the communication of the schedule plus w r times the number of renegotiations, and the, which is dened as the sum of the V i in Figure 1. The time units are seconds, and the volume units are cells. Throughout the analysis, w r has a value of (cells), corresponding to the communication of a 1Mbit/s link for the length of about 6 polling intervals. With this it does not pay o to renegotiate after each polling interval. Figures 4 and 5 show the simulation results for Trace 1 and Trace 2. Shown are and (as dened above) for dierent parametrisations of the on-line heuristic. The line \cr " connects the (/) points produced by the critical region heuristic with c r = 6746:95 and c d varying inside [0.0003, ]. The line \cr " connects the (/) points produced by the critical region heuristic with c r = 80963:4 and c d varying inside [0.004, 4.63]. The line \no reneg" connects the (/) points produced by the constant bit rate schedule for bit rates in f1, 1.5, 2, 2.5g Mbit/s. Also shown are the results from optimisation, when w r was set to and w d varies inside [0.013, 4.63]. The reason that the optimal algorithm is not able to achieve zero, is that its input was not the original input trace, but the trace whose values were discretised to multiplies of. The of the output schedule was computed using the original undiscretised trace. For small c d values, produced by the on-line heuristic can vary unpredictably depending on the location of the peaks in oered trac But in general decreases for decreasing c d. This behaviour is seen in the fussy line in Figure 5, The simulation results for the heuristics lie approximately half-way in between the constant bit rate schedule and the optimal schedules, no matter how one weights s against. For instance, with appropriate parameterisation the on-line heuristic is able to produce much lower s than the constant bit rate schedule of 2 Mbit/s, but with approximately the same. For Traces 3 and 4 we compared results from trac experiments and simulation. The values of c r and c d used in this analysis are listed in Table 2. Note that c r and c d control the times that the critical region heuristic waits before negotiating upwards or downwards. More specically, c r, c d, and the mean length of the polling interval t

8 5e+08 4e+08 cr cr no reneg op e+08 4e+08 cr cr no reneg op e+08 3e+08 2e+08 2e+08 1e e+07 8e e+08 1e e+07 8e e+08 Figure 4. Simulations with Trace 1 Figure 5. Simulations with Trace 2 determine the number j of polling intervals that the heuristic waits before proposing a downward renegotiation by = 0:5 Mbit/s. They also determine the number k of polling intervals that the heuristic waits before proposing an upward renegotiation. The values of c r, c d and the corresponding numbers j and k used in the experimental platform are listed in Table 2. Table 2 Parameters used for trac experiments c r c d j k Figure 6 shows the results of the trac experiment for Trace 3. Each parameter setting in Table 2 was tested four times. The points denoted by \cr exp" belong to the experiments with c r = 6746:95 and the two dierent c d -values. It is easy to distinguish the set of four experiments belonging to c d =0:01207 from the set of four experiments for c d = 0: In general, the larger c d, the smaller the and the larger the. Moreover, Figure 6 shows the experimental results for the constant bit rate schedules with bit rates in f2; 2:5; 3; 3:5g Mbit/s. As one sees, the critical region heuristic with c r = 80963:4 and c d =2:3166 was able to improve both the and the as compared to the constant bit rate schedule of 3 Mbit/s. Figure 7 shows the simulated results for the same parameter setting as used for the trac experiments. Comparing Figure 6 and Figure 7, one sees that the points have approximately the same relative position with respect to each other, and that and values for the same parameter setting have about the same order of magnitude.

9 The same experiments and simulations were done also for Trace 4, a trace with relatively little activity. The results for the trac experiments are shown in Figure 8 and for the simulation in Figure 9. Here, the constant bit rates were chosen as f1:5; 2; 2:5g Mbit/s. The on-line heuristic performs comparable to the constant bit rate strategy, especially for c r = w r. In simulation, a renegotiation action is immediate while in the experiments the actual mechanism to perform the renegotiation is to tear down the connection and build a new one. This action will interrupt packet transmission for approximately 0.5 seconds, giving rise to the dierences observed in between experiments and simulations. This eect is most pronounced in Figure 8, where total is low. Further experiments (simulations and trac experiments) made with other trace samples conrm the following. For bursty trac, the critical region heuristic with c r = w r is able to close part of the gap between the constant bit rate schedule and the optimal schedule. The heuristic with a peak rate discretisation of 0.5 Mbit/s performs considerably better than with a discretisation of 1 Mbit/s. For small c d values, can vary unpredictably in dependence of c d, but in general the sum of communication and renegotiation s decreases when c d is decreased. 5e+07 cr exp cr exp no reneg exp 5e+07 cr sim cr sim no reneg sim 4e+07 4e+07 3e+07 3e+07 2e e+07 4e+07 6e+07 2e e+07 4e+07 6e+07 Figure 6. Experiments with Trace 3 Figure 7. Simulations with Trace 3 7. Conclusion Our goal was to design an algorithm that is able to assist the user in renegotiating the capacity of an ATM link with exible trac (e.g., TCP/IP) by making a tradeo between communication s, renegotiation costs and the user's sensitivity to long-term s. The algorithm operates solely on observed send rates and does not need any information about buer backlogs. The algorithm was tested by simulation and in an experimental

10 2.4e+07 2e+07 cr exp cr exp no reneg exp 2.4e+07 2e+07 cr sim cr sim no reneg sim 1.6e e e e+06 4e+06 6e+06 8e e e+06 4e+06 6e+06 8e+06 Figure 8. Experiments with Trace 4 Figure 9. Simulations with Trace 4 environment. The algorithm's performance in terms of and was compared to the performance of an optimal o-line renegotiator (with knowledge of the complete trace) and of a simple constant bit rate strategy. The heuristic described in this paper is apparently able to make a controlled dynamic trade-o between communication costs and costs. The considered algorithm retains its properties also when used with realistic trac. As the algorithm can work with charging management systems, it is of practical relevance. The testbed may as well serve to evaluate and compare other on-line heuristics. It may also serve as a model for more complete tests with several TCP/IP sources and more involved network scenarios. We assume that the on-line algorithm can also be applied to the renegotiation of trac contracts for end-to-end guaranteed services for users that are more -sensitive than the operator of an ATM link. In this case the agent implementing the algorithm might additionally have access to user's preferences for throughput or it can even measure on-line. The performance of the on-line algorithm described in this section will have to be assessed anew in this situation. REFERENCES 1. R. Andreassen, M. Stoer, and O. sterb, Charging ATM Internet Access, an Experiment of Usage Based ATM Charging. In Colloquium on Charging for ATM the Reality Arrives. IEE, London (1997). 2. E. W. Zegura and S. McFarland and O. Parekh, A Survey and New Results in Renegotiated Service, Journal of High Speed Networks 6 (1997) 197{ W. Almesberger, L. Chandran-Wadia, S. Giordani, J.-Y. Le Boudec, and R. Schmid, Using Quality of Service Can Be Simple: Arequipa with Renegotiable ATM Connections. Computer Networks and ISDN Systems 30 (1998) 2327{ M. Grossglauser, S. Keshav, and D. Tse, RCBR: A Simple and Ecient Service for Multiple Time-Scale Trac. IEEE/ACM Transactions on Networking 5 (1997) 741{ 755.

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