On Mean Rate Policing with a Bursty Traffic Specification & Allocation (BTSA) Policer Function

Transcription

1 On Mean Rate Policing with a Bursty Traffic Specification & Allocation (BTSA) Policer Function Tariq M. Jadoon & David A. Harle Communications Division, Department of Electronic & Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, UK. Tel: Ext. 08 Fax: tjadoon@comms.eee.strath.ac.uk D.A.Harle@comms.eee.strath.ac.uk ABSTRACT This paper evaluates the performance of a Bursty Traffic Specification & Allocation (BTSA) policer function as a mean rate policer for packet voice, still picture video services and on-off sources with arbitrary distributions of the off periods. Scenarios considered include varying the mean burst duration, mean silence period, etc. over nominal values based on a MMDP model of packet voice and still picture video services. For on-off traffic models with arbitrary distributions the squared co-efficient of variation of the off periods is varied such that the mean rate remains constant but the squared coefficient of inter arrival times of cells varies. The study investigates the effectiveness of the BTSA policer for mean rate policing. The work discusses and compares the results produced in previous studies using analytical and simulation techniques. Introduction The Asynchronous Transfer Mode (ATM) offers a flexible solution to the diverse requirements of an Integrated Broadband Network (IBN). It is envisaged that services with a broad range of traffic characteristics will be statistical multiplexed onto a common resource. It is hoped that the statistical multiplexing the traffic cell streams will make it possible to dynamically allocate bandwidth on demand. Resource Allocation to guarantee the negotiated Quality of Service (QoS) will be based on the traffic contract between the user and the network. The traffic contract takes place during the connection establishment phase. The traffic contract, as specified in ITU-T Recommendation I.371 [1], consists of the connection traffic descriptor, the requested QoS class and the definition of a compliant connection. Usage parameter control (UPC) or policing functions will ensure that the network users conform to their traffic contract, i.e., the parameters defined for that connection at call set-up. This ensures that the unintentional or malicious behaviour of some users will not result in a performance degradation for other users. An ATM cell stream generated by a customer will be subjected to UPC functions at the ATM User Network Interface (UNI) before it is allowed to enter the public ATM network and at Network Network Interfaces (NNIs) between networks by the network providers. Policing may also take place at the customer premises access network if the implications of breaking the traffic contract are severe. This implies that the tariff structure will play a major role in shaping ATM customer cell streams. It has been shown that the effective bandwidth of a source just depends on the customer's expected mean rate []. Thus, policing the expected mean rate, although believed by some to be impractical, would result in a more efficient utilisation of network resources provided that the customers adhere to their expected mean rates for the duration of the call. 3/1

2 Basic Requirements for Policer Mechanism The UPC function will extract essential information from the cell header, i.e. the connection identifier (VPI/VCI number) and the cell loss indicator (CLP bit). With this information, it will test the validity of the cell and take a decision about its fate. Ideally, the policing mechanism should be transparent for those connections that respect their traffic contract. On the other hand, it should rapidly detect any violating traffic and act by discarding/tagging cells or in extreme cases dropping the connection altogether. This intelligent function which separates conforming functions from non-conforming cells is called the police criterion calculator (PCC) [3]. Numerous mechanisms (criteria) have been proposed. They most commonly involve [4]: window method, which limits the number of cells in a time window a leaky bucket method, which increments a counter for the arrival of each cell and periodically decrements this counter. The optimum dimensioning and effectiveness of a policing mechanism depends heavily on the source traffic characteristics and its QoS requirements. There are two fundamentally opposite approaches for specifying traffic parameters. One approach is a statistical approach based on the stochastic traffic parameters and the other is an operational approach defined by means of a rule [5]. Deterministic rule based traffic descriptors offer advantages over statistical based traffic descriptors. In the main, it is difficult to estimate the statistics of real time traffic a priori without monitoring the traffic over long periods of time in order to detect, with some confidence, whether the negotiated parameters of the traffic contract have been respected. There are two fundamental problems, which give rise to a certain probability of incorrect policing decisions, with respect to mean rate policing, which have been discussed in previous literature [6-8]. The characteristics of the source must be estimated on the basis of a relatively short sample. A large sampling time increases the reaction time of the policing mechanisms. Inaccuracies and uncertainties in the knowledge about relevant parameters, in the establishment phase of the call, cause the margins between the policed bit-rate and the actual bit rate to increase. This results in a loss of effectiveness of the policing mechanism. The mean bit rate can be abstracted from historical information or measurement. When policing a single VC, it is possible at call set up for the user to declare the type of service that they require. With this information the network dimensions its policing mechanisms according to a set of default nominal parameters that have been established through modelling and/or measurement for that particular type of service. If the source deviates from these nominal parameters, the policing mechanism comes into action by marking or dropping cells. ATM Connection Descriptors According to the ATM-Forum User Network Interface Specification [10], an ATM connection can be described by four parameters: the peak cell rate (PCR), the cell delay variation (CDV) tolerance, the sustainable cell rate (SCR) and the maximum burst size (MBS). A reference constant bit rate stream (CBR) may experience CDV due to actions of the ATM layer such as cell multiplexing, physical layer overheads, insertion of operation and maintenance (OAM) cells, etc. As a result, policing mechanisms may observe some cells arriving at a higher bit rate than the declared PCR. This necessitates the consideration of a CDV tolerance for the policer. A variable bit rate (VBR) connection will be characterised by both a PCR and a SCR. VBR traffic is bursty in nature, i.e. the PCR is different from the mean cell rate. This means that a source may transmit at the PCR for a while and then transmit at a lower rate or not transmit at all for a while. The maximum size of the burst at the PCR is the MBS. 3/

3 Traffic Source Models Packet Voice & Still Picture Video Services A two-phase burst/silence model shown in Fig. 1 has been used for evaluating the effectiveness of the BTSA policing function as a mean rate policer. This model has been used in earlier publications [7-9] for packetised voice and still picture video services. The cell arrival process can be characterised as Markov Modulated Deterministic Process (MMDP). During the burst phase, the source emits cells at a constant cell emission rate b, i.e. the PCR, for a negative exponential distribution of time with mean h. The burst is then followed by a negative exponential distributed silence period with mean k. The traffic sources can be characterised by the following set of parameters: peak (burst) cell emission rate [b] mean burst duration [h] mean silence duration [k] mean cycle duration [c = h+k] Table 1 mean source burstiness [X = (h+k)/h] mean source cell rate [ m = b.h/(h+k)] mean burst length in cells [t = b.h] Traffic Parameters MMDP h k Parameter Packet Voice Still Picture b 83 cells/sec 508 cells/sec h 35 ms 500 ms burst silence k 650 ms ms m 9 cells/sec 604 cells/sec Fig. 1: Two-phase Burst Silence Source Model X.85 3 Table Table summarises the traffic source characteristics for packet voice and still picture video services. On-Off Traffic Models with Arbitrary Distributions It has been suggested that future ATM traffic will be better characterised by two alternating on and off periods [11]. Initial results [1] from high performance computing networks like the VISTAnet Gigabit Network indicate that the active period has a constant distribution while the silence period may be characterised by a uniform, geometric or hyper-geometric distribution. Following a similar analysis to that described in [11], consider an on-off traffic model with a constant on period and a uniform off period. The model can be characterised by the following parameters: burst length (h M ) slots minimum off time (k m ) slots ( km km + 1) 1 maximum off time (k M ) slots var (off) = 1 k mean off time k = M + k m ( k 1 1 slots cs M km + ) = 3( km + km) Table 3 Traffic Parameters 3/3

4 In Table, var(off) is the variance of the off times and (c s ) is the squared co-efficient of variation of the off times i.e., variance/mean. The mean cell rate (m) in cells/slot is given by hm m = hm + k A surprising result from [11] shows that the squared co-efficient of variation of the inter arrival times of cells, which is a good measure of the burstiness depends on only the first two moments and not on the shape of the independent renewal distributions of the on-off times. The BTSA Policer The bursty traffic specification and allocation (BTSA) approach simply consists of a two stage continuous state leaky bucket policer [13]. The leaky buckets of the BTSA policer are in cascade (Fig. ). The user specifies the PCR, the expected average or SCR and a MBS. The network uses these parameters to set up a two stage policer. In the first stage, the peak rate monitor tests any violations to the PCR. In the second stage, a leaky bucket with a leaky rate equal to the SCR and the capacity of the bucket associated with the MBS polices the mean bit rate and maximum burst size. (1) ATM cells N = Bucket size a = Leaky rate Fig. : N1 a1 N a Peak rate monitor Mean rate monitor BTSA Policer Mechanism The Leaky Bucket Mechanism The virtual scheduling algorithm and the continuous state leaky bucket are two equivalent versions of a parameterised conformance testing algorithm which have been proposed in ITU-T Recommendation I.371 [1] to cope with cell delay variation (CDV). The continuous state leaky bucket consists of a counter which is incremented by arriving cells and decrements periodically as long as the value of the counter is positive. If the instantaneous cell arrival rate is greater than the decrementation rate, the counter value starts to increase until a pre-defined upper limit. Suitable action (e.g. discarding or marking) is taken on any subsequent cells until the counter has fallen below its limit. The increase in the value of the counter is analogous to a bucket filling up and an upper limit for the counter to the capacity of the bucket which results in spill over when overfilled. Dimensioning the Buckets The Peak Rate Monitor Previous works [6,14-15] have analysed the CDV caused by various topologies in the access network (e.g. FIFO multiplexors, buses, etc.) and have given some typical values that could be used as defaults for the bucket depths required to achieve a given target cell loss probability within a CDV tolerance. Their results suggest that CDV mainly depends on the load on the access multiplexor. The analysis in [6] consists of a single reference Constant Bit Source (CBR) connected to a simple First-In-First-Out (FIFO) queue offered various streams of traffic. This is motivated by the use of simple multiplexors and the fact that a switch can be modelled as a transparent cross connect with output buffers. The results indicate the worst case CDV, i.e. the CDV when the multiplexor is running at full load and the background traffic is Poissonian. The analysis uses the Kingman bound [16] for the tail behaviour of GI/G/1 queues in heavy traffic which can be applied to GI/D/1 queue to calculate the bucket size for a given target cell loss probability. This 3/4

5 effectively means that if the bucket depths are set using a fixed leaky rate, with a given cell loss target, the source can be policed and, thus, guarantee that the losses will not be more than the cell loss target. If we set the leaky rate a to 95% efficiency, theoretically it would be possible for a stream with a constant cell rate of 5% higher than the peak cell rate to pass through the policer unchecked. Due to the clumping and dispersion of cells caused by the multiplexing devices and other network functions we have to account for CDV. Thus setting a = b/0.95, we get a CDV tolerance of 0.6 ms, and bucket depths of and 4 for the packet voice and still picture services respectively and using the analysis from [6] a target cell loss probability of Working at higher efficiencies, e.g. 99% would not be fruitful as the CDV tolerance would go to an unacceptably high values. Mean Rate Monitor In [8] we see that, for a given set of nominal source parameters, to obtain an acceptable less loss probability at nominal conditions, the size of the LB threshold counter is very high. For the case of Packet Voice it is 98.5 t o or 881 cells at a leaky rate of a = 1.09m o. Similarly for Still Picture, we have 3.01t o or cells at a leaky rate of a = 1.1m o. Clearly these values for the threshold counter are very high and would result in a very slow reacting policing mechanism. One option is to increase the leaky rate of the mean rate policer and reduce the value of the threshold counter, such that we still have a target cell loss probability of less than 10-6 for the nominal parameters. RESULTS Packet Voice & Still Picture Video Services The effectiveness of the BTSA policer can be evaluated by varying the source traffic parameters over the nominal source parameters. Ideally the cell loss probability should be close to 10-8 for the nominal parameters and be the exact fraction of violating cells for peak and mean bit rates greater than the nominal values. There are two scenarios for which the tests were performed for packet voice and still picture video services. The mean burst duration h, of the source, is varied over the nominal burst duration h o, such that the burst cell rate b o remains constant. This is effectively an increase in the mean cell rate m over the nominal mean cell rate m o. The mean silence duration k, of the source, is varied over the nominal silence duration k o, such that the burst cell rate b o remains constant. This is also, in effect, an increase in the mean cell rate m over the nominal mean cell rate m o. Simulation results for the case of a threshold counter equal to 0 t o and a leak rate a = 1.m o are given for packet voice and still picture services in Fig. 3 and Fig. 4 respectively From the results shown in Fig. 3 and Fig. 4, it can be seen that for a BTSA policer function, the cell loss probability is 10-7 for nominal parameters and increases dramatically for changes in the aforementioned parameters over the nominal values. This demonstrates the ability of a BTSA policer to perform mean bit rate policing effected by changes in the mean burst h and silence duration k, while the burst cell rate remains within the peak policed cell rate. Thus, by dimensioning the two stages of the BTSA policer, such that the peak rate monitor has a fast reacting leaky bucket with a small bucket size and a leaky rate close to the peak cell rate and the mean rate monitor has a large bucket size and a leaky rate slightly higher than but close to the mean cell rate, we can satisfactorily achieve peak and mean rate policing for packet voice and still picture video services. 3/5

6 Fig. 3: BTSA Performance characteristics (CLP Vs. m) for Packet Voice service. Fig. 4 BTSA Performance characteristics (CLP Vs. m) for Still Picture service. 3/6

7 On-Off Traffic Models with Arbitrary Distributions Consider a BTSA policer with its leaky buckets dimensioned such that the maximum burst size that can pass through the policer at the peak cell rate is (h M ). For no cell loss to occur, k m k bound, where k bound is the time required (expressed in slots) to empty the mean rate monitor after the completion of a burst. k bound = h M ( 1 a), () a (recall that a is the leaky rate of the mean rate monitor of the BTSA policer). Defining x as the width of the uniformly distributed off period, i.e. x = k M - k m. The cell loss probability (CLP) can be expressed as: max 0, k k max 0, k k x bound + bound m CLP = or x x Assuming a constant on period of 40 slots and a uniform off period with a mean equal to 100 slots. Fig. 5 shows the CLP expressed as a function of the width x, for leaky rates a, ranging from 1.05m to 1.3m. From Fig. 5, it can be observed that there is great variation in the CLP as the variance of the off periods changes. Thus, cell streams having the same burstiness as defined by the peak/mean cell rate but different widths of the off period would require different leaky rates in the mean rate monitor to achieve no cell loss for nominal parameters. The SCR dimensions a. For cell streams with a low to moderate x/k, the SCR is comparable with the mean cell rate m. (3) 0.5 CLP Vs x for a = (1.05m -1.3m) 0.4 m1 05 ( x) m1 1 ( x) 0.3 CLP m1 ( x) m1 3 ( x) x width (x) Fig. 5: Cell loss probability Vs width x for h M = 40 slots, k =100 slots These results can be extended to on-off traffic with off period distributions which are symmetrical about their mean. The CLP would be given by probability that the off period is less than k bound. The BTSA policer can detect changes in the mean rate when variations in the traffic stream cause k m to reduce below k bound. Thus, it can effectively police the mean rate if the variance or squared co-efficient of variation of the off period does not significantly change during the course of the connection. However, it would be 3/7

8 ineffective in detecting an increase in the mean cell rate if the mean off period and the width x decreased simultaneously such that condition for no cell loss, i.e., k m k bound, is not violated. For geometrically distributed off periods with a mean off time k slots. The probability that an off period is N slots in duration is P[k = N] = pq N-1, where p = 1/k, q = 1-p and N = 1,,3,... Once again, if k bound is defined as the time required expressed in slots to empty the mean rate monitor after the completion of a burst. The probability of cell loss can be evaluated as: kbound p q n= 1 Summing the simple geometric series (4), results in: n 1 (4) CLP = 1 q kbound (5) For example consider a constant on period of 40 slots and a uniform off period with a mean equal to 100 slots. The CLP from (5) would be 0.51 for a= 1.3m and 0.01 for a = 3.33m. Thus, if the BTSA policer's monitors are dimensioned such that the maximum burst size that can pass through the policer at the peak cell rate is MBS, and the mean rate monitor has a leaky rate equal to the SCR, which is set slightly greater than the mean cell rate of the source. The CLP, for constant on periods and geometrically distributed off periods, is unacceptably high. In this case, it is not possible to reduce the CLP to below 10-7 for nominal parameters by increasing the SCR. For nominal parameters, the CLP could be reduced by increasing the virtual bucket size of the mean rate monitor, but doing so would result in the possibility of bursts longer than what have been contracted, entering the network unchecked. This renders the BTSA policer incapable of handling traffic with constant on periods and geometrically distributed off periods. CONCLUSIONS The effectiveness of a BTSA policer has been evaluated for packet voice, still picture video and on-off traffic with constant on periods and uniform or geometrically distributed off periods. It has been observed that by dimensioning the two stages of the BTSA policer such that: the peak rate monitor has a small bucket depth and its leaky rate set slightly higher than the peak cell rate to account for CDV, the mean rate monitor has a large bucket size with a leaky rate set slightly higher than but close to the mean cell rate, We can satisfactorily achieve peak and mean rate policing for packet voice, still picture video services and on-off traffic with constant on periods and uniformly distributed off periods provided that the variance of the off periods does not significantly change during the duration of the call. However, for on-off traffic with constant on periods and geometrically distributed off periods the BTSA policer cannot be simultaneously dimensioned to police a MBS and a mean cell rate. REFERENCES [1] ITU-T: Recommendation I.371. 'Traffic Control and Congestion Control in B-ISDN', Geneva [] F.P. Kelly, "Tariffs, Policing and Admission Control for Multiservice Networks", 10th UK Teletraffic Symposium, [3] Kees van der Wal et. al., "Implementation of a Police Criterion Calculator based on the Leaky Bucket Algorithm", IEEE GLOBECOM'93, pp /8

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