6A.2.1 ABSTRACT DIMENSIONING CRITERIA FOR POLICING FUNCTIONS IN ATM NETWORKS. P. Castelli (*), A. Forcina (+), A. Tonietti (*)

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1 DIENSIONING CRITERIA FOR POLICING FUNCTIONS IN AT NETWORKS P. Castelli (*), A. Forcina (+), A. Tonietti (*) (*) Cselt, Via G. Reiss Romoli 274, Turin, Italy (+) Sip Headquarters, Via della Vignaccia 45,00196 Rome, Italy ABSTRACT The paper is devoted to discuss some basic issues relevant to the policing function (or, compliant with the CCITT vocabulary, Usage Parameter Control function) in AT networks. ore preclsely, the problem of controlling the source peak rate in presence of the cell delay variation, introduced in the customer premises network, is considered. Firstly, a model for analysing the cell delay variation is presented, under the assumption of a constant bit rate source multiplexed with a Poisson stream. Then, on the basis of the obtained distribution, the relevant parameters of two policing devices (the Jumping Window and the Leaky Bucket) are dimensioned. The presented numerical results lead to the conclusion that the leaky bucket allows a tighter source control than the jumping window. I. INTRODUCTION The Asynchronous Transfer ode (AT) technique has been recognized as the transfer mode to be employed in the future Broadband ISDN (B-ISDN) [ 11 because of, among others, its characteristics of high flexibility in providing a wide range of telecommunication services. This feature, indeed, is achieved by means of "on demand" dynamic bandwidth allocation and the performing of only the routing function within the network. A discussion on all the pros and cons characterizing the AT technique is out of the scope of this paper but, on the basis of the mentioned capability, an aspect is worth mentioning. If, on the one hand, AT provides customers and telecom operators with a highly flexible and integrated tool for service offering and network operation, on the other hand, it requires new and sophisticated procedures for trafic control and network resource management. This paper limits its scope to one of the presently foreseen traffic control capabilities. In particular, some issues relevant to the so called "policing" function (or compliant with the CCI'ZT vocabulary, Usage Parameter Control (vpc) function) in B-ISDN are addressed. As for the definition of the UPC function and its importance for an efficient and "safe" traffic management, it is useful to quote CCITT Rec. I. 311 [2] which states that UPC is "the set ofactions taken by the network to monitor and control (user's) trafic in terms of traffic volume and cell routing validity". In other words, since the user can negotiate with the network the bandwidth of a given connection, which in general represents a percentage of the total link capacity, it is mandatory to monitor and control that the received amount of information does not exceed the agreed values of the relevant traffic parameters. If this function is not performed, unexpected cell flows can, intentionally or unintentionally, "flood" the network causing catastrophic congestion states. It is worth emphasizing two remarks about the previous definition. The first one is relevant to the location of the UPC unit. Even though in the past, many papers [3, 41 have been presented proposing to control the traffic directly at the source, CCITT SG XVIII has clearly identified [2] the location of UPC at the User-Network interface, where a virtual channellvirtual path link is terminated. The second one calls for the level of standardization for the UPC function. In order to achieve a trade-off between the level of freedom to be left to the network operator's policy and the need of a clear and unambiguous specification, it is desirable that a detailed specification of the algorithm, without numerical values of the related parameters, be agrecd in CCllT. The peak rate is the most important source parameter to be enforced, because it should be controlled for any source type (constant, variable or on/off bit rate). oreover it is mandatory to implement this control even if. in the first AT realisations, a simple peak rate allocation is adopted for any service. As pointed out by some papers 15, 6, 7, 81, even the apparently simple enforcement of the peak rate of a constant bit rate (CBR) source is complicated by the fact that the periodic cell stream emitted by the source can be altered by the random delays introduced in the multiplexing stages, located in the customer premises IN FOCO '92 6A.2.1 CH $ IEEE 0759

2 network, between the source and the UPC unit. On the basis of these considerations, the paper presents an analysis of the effects of the cell delay variation (CDV) on the performance of two UPC mechanisms (the jumping window and the leaky bucket). used for enforcing the peak rate. In section 11. a model for the CDV analysis is presented, under the hypotheses of a CBR source multiplexed with Poisson traffic on a discrete-time (+D)/D/l queue. In section 111, on the basis of the obtained distribution of the CDV, the relevant parameters of the mentioned UPC mechanisms are dimensioned. Some numerical results, useful for comparing the efficiencies of the two mechanisms, are presented in section IV. In section V the conclusions of the paper are summarized. 11. CELL DELAY VARIATION ANALYSIS The CDV is intended to capture all the alterations of the traffic characteristics of a connection introduced by the AT layer functions. A clear definition of the CDV has not yet been agreed in the standardization bodies. In this paper it is assumed to be defined as the diference between the delays experienced by two generic cells belonging to the same connection. Since this analysis aims at evaluating the effect of CDV on the UPC function, the attention is focused on the CDV introduced in the B-NT2 due to the asynchronous multiplexing of different traffic streams on the same physical access link (Fig. 1). Public network In particular, the CDV introduced on a periodic stream of cells is evaluated on the basis of an analytical model [9, The following basic assumptions are Used: i) ii) iii) iv) v) the multiplexing of different streams inside the B-NT2 is modelled as a discrete-time {+D)/DIl queue with infinite buffer capacity. The queue is served according to a FIFO discipline; the global arrival process, excluding the specific periodic stream under study, is Poisson. ore precisely, the number of arrivals in each time-slot are distributed according to independent and identical Poisson distributions; the inter-arrival time at the B-"I2 between two consecutive cells belonging to the considered stream is constant and equal to d; the analysis is carried out under the steady state; the time unit is equal to a time-slot. Let J,, be the CDV between two cells belonging to a given connection, and spaced by n - I cells of the same connection. According to the above definition, it can be computed as: where W; and Wi+,, are the delays experienced by the two cells inside the B-NT2. As Wi and Wi+, are correlated, the computations of the probability distribution are performed conditioning J,, on: 0 ii) the queue state found by the first arrival; the number of anivals occurred in the same slot of the first arrival; iii) the position of the first arrival in the amval batch; 2JL User premises network Fig. 1 Reference configuration of the User-Network Interface 1 iv) 4 be state transition performed by the queue in nd time-slots; the position of the second arrival in the arrival batch. A limit distribution. overestimating the actual one, can be found by assuming the two observed cells are spaccd by an infinite interval of time. In this case the state of the queue at the time of the second arrival does not depends on its state at the time of the first arrival, so that the delays experienced by the two cells are independent and the CDV distribution can be computed A.2.2

3 by the convolution of the delay distributions. The model has been solved for thrcc classes of CBR sources, for different values of the global offered load p: i) low speed sources, with cell intcr-arrival time d = 1500 slots (i.e. 0.1 bps on a link of 150 bps); ii) medium speed sources, with cell intcr-arrival time d =150 slots (i.e. 1.0 bps on a link of 150 bps); iii) high speed sources, with cell inter-arrival time d = 15 slots (i.e bps on a link of 150 bps). For each of these classes the limit distribution (plain line) and the one corresponding to two consecutive cells (dashed line) are plottcd in Fig. 2 (p = 0.7) and in Fig. 3 (p = 0.9). the faster the convergency is. The limit distributions have a typical double-geometrical shape, whose spread increases with the offered load and it is also slightly dependent on the connection bandwidth: this is due to the fact that the status of the (+D)/D/I queue, for a fixed value of p, depends on the amount of deterministic traffic. lxlo0 I I I I 1x10-' 1x10-2 1x10-3 1x10" 1x10-5 1x10-6 1x10-7 1x108 1x10-9 lxlo"o Time slots Fig. 3 Distribution of the cell delay jitter p = 0.9 Aiming at dimensioning a UPC mechanism, it is helpful LO introduce some other random variables related to the CDV. Following [9] and referring to Fig. 4 we define: Fig Time slots Distribution of the cell delay jitter p = 0.7 On the basis of the achieved results some considerations can be drawn. The distribution of the CDV mainly depends on the global offered load and on the distance between the two observed cclls. oreover its mode and mean are both equal to 0. Focusing on a given connection and fixing p, LIE distribution tends to the corresponding limit one as the distancc between the two considered cells increases. The narrower the connection bandwidth and the lower the offered load are. i) The inter-exit time between two generic cells of the same connection: Z,, = n d + Wi+,, - Wi = n d + Jn (2) ii) The probability mass and the cumulative distribution function of the inter-exit time: f,,(x) = Pr (Z, = x) = Pr (Jn = x - n d) (3) F,(x) = Pr (2, I x) iii) The probability mass distribution function of the first exit time Z1' with respect to an arbitrary origin to : (4) 6A

4 as known from the renewal theory. variable or on/off bit rate) even if a simple peak rate reservation scheme is adopted for resource allocation. Even though the problems related to the peak rate control were often underestimated in the past [12, 131, recent papers [5,6,7,8] have pointed out that the CDV introduced by the B-NT2 in the controlled stream makes this enforcing action complicated, even in the apparently simple case of a constant bit rate connection. oreover, in [5. 81 the dramatic impact on the network efficiency of an enforcement action not enough accurate has been shown. Therefore it is very important to find reliable methodologies for dimensioning the UPC devices and for cvaluating their performances. As for the dimensioning, it can be worked out by fixing some of the following conditions: i) the probability of discarding a conforming cell; ii) the percentage of allowed overload; Fig. 4 Departure process of the deterministic stream from the (+D)/D/l queue iv) The probability mass and the cumulative distribution function of thc number of cells (of the monitored connection) leaving the queue in an interval of length T slots starting at the arbitrary origin to: gdn) = Pr (nt = n) (9 Following [9] we have: Pr(nT2n)=Pr(Zi+Z,.l<T)= = I - Pr (nt< n) = I -Pr (ntin-i) = = I - GT (n - 1) from which it follows: 111. PEAK RATE UPC ALGORITHS The enforcement of the peak rate is a crucial point of any congestion control scheme for AT networks, since it represents the first and simplest way of preventing the network from being overloaded and should be implemented for any sourcc type (constant, (8) iii) the probability of accepting a non conforming cell: iv) the response time in case of a contract violation. Taking into account that any control algorithm has only a limited set of design parameters. it is clear that not all these conditions can be fixed at the same time. The first two are by far the most important ones, being directly related to the transparency of the algorithm (with rcspcct to conforming traffic) and to its accuracy, respcctively. As for the performance evaluation, special attention should be given to the characterization of the "worst case truflc" getting out from the device (i.e. the one with the greatest burstiness) because, to guarantee an effective protection of the network against congestion, this traffic is thc one to be considered by the call admission control func Lions. For many UPC algorithms, and in particular for the ones considered in this paper Cjumping window and leaky bucket), such worst case traffic is represented by an onloff process (Fig. 5) with deterministic burst and silcnce lengths, peak rate equal to the access link rate and average rate equal to the enforced source peak rate (the declared source peak rate plus the allowed overload). This traffic can be generated by sending cells at the link rate till the UPC mechanism reaches the discarding thrcshold (e.g. the maximum number of cells in a window for the Jumping Window or the bucket size for the Leaky Bucket) and then stopping till it drops again to the initial condition. It is worth noting that, being the peak rate of the outgoing traffic equal to the link rate, the burst length (measured in time slots) is equal to the number of cells transmitted by the source during the on pcriod, and givcs an indication of the rcsponse time of the device. A further remark is relevant to the burst A.2.4

5 period: this parameter represents the minimum interval of time during which the device must control the arrival process to guarantee the effectiveness of the enforcing acrion, and can be considered the "time constant" of the device. 1) the probability of rejecting a conforming cell lower than a; 2) the average allowed rate lower than B,(l +p), where B, = I/d is the source rate agreed at call set up and p is the hction of allowed overload. I, Burst period d Rcfcrring to the distributions introduccd in section 11, the probability of rejecting a conforming cell is given by formula (9). Then the first condition can be expressed as: Fig. 5 The "worst case traffic" getting out from the UPC device In addiction to the worst case traffic, other useful performance parameters not considered in the paper are: i) Statistical accu racy: the probability of detecting a non-conforming sourcc. ii) Imdementation cost. In the following, two classical mcchanisms will be dimensioned and evaluated on the basis of the previous criteria: the jumping window and the leaky bucket. A) The JumDine Window T nt<n Fig. 6 T nt<n The Jumping Window In the jumping window mwhanism [8, 9, 141 (Fig. 6) the arrival process is observed for an interval of fixed length T and up to n cells are allowcd to enter the network during this interval. If more than n cells are detected the source is considered to bc non conforming and the excess cells are either discarded, or tagged, by the device. Each window begins exactly at the end of the previous one and the starting time can be considered generic with respect to the phase of the controlled SOUrCe. According U) the dimensioning criteria stated in the previous section. n and T should be fixcd in order to make: and the second one as: n T IB, (1 + PI (12) As for the performance evaluation, it is worth noting that the user may exploits the transmission capability of two consecutive windows as a whole, by sending n cells at the end of a window and then n more cells at the beginning of the next one without interrupting the transmission. Therefore, for the jumping window mechanism the worst case traffic exhibits the following characteristics: i) the burst lenglh is equal to 2n. ii) the burst period is equal to 2T; --*mm I I FRO THE SOURCE I Fig. 7 I mm0l SIGNAL DROPPING SWCH The Leaky Bucket b TOTHE NETWORK The Leaky Bucket [15] (Fig. 7) is a counter which is incremcnted each time a cell is received from the source and is decremented with a constant leaky rate U. The counter is neither decremented below zero nor incrcmented above a given upper threshold (bucket size). A cell arriving when the counter is below the bucket size is considered compliant and transmitted forward. On the other hand, a cell arriving when the countcr is equal to the bucket size is either discarded, or 6A

6 tagged, by the device. The flow of accepted cells (compliant plus tagged) is not altered by the device. The problem of dimensioning the leaky bucket for the peak rate conuol, taking into account the effects of the CDV, has been examined by several authors [7. 11, 163 according to different approaches, but all of them neglect the possibility of the bucket being empty during the observation time, which leads to underestimate the bucket size and the role played by the leaky rate. Such approximation is removed in this paper where the Leaky Bucket is modelled as a discrete time GIDII l queue and an exact solution of the model is found under the assumption that the number of arrivals in each macro-slots are distributed according to independent and identical distributions. A macro-slot represents the time unit for the analysis of the queue and its duration is equal to the qucuc service Lime, i.e. the time required to transmit a cell at the leaky rate (I la time-slots). The distribution of the number of arrivals in each macro-slot is given by formula (6) computed for T = I la. The hypothesis of independence of the number of arrivals in each macro-slot implies the independence of the state of the multiplexer originating the cell stream in two successive time instants at distance Ila. This assumption is reasonable if the leaky rate is a small fraction of the link rate (e.g. c 0.1) and, in any case, leads to a conservative evaluation of the bucket size. Under these assumptions the Leaky Bucket can be modelled as a arkow chain with +I states and the state probability P(x) can be found by solving the state equation: U P(x) = P(O)gl/*(X) + K(Y) gll*(x-y+l) (13) y=l with the constraint: CP(x) = I x=o Let introduce now the auxiliary variable K(x), such that: P(x) = P(0) K(x) (15) the normalization condition (14) givcs: I P(0) = (I + 2 K fx) ) x=l (16) Finally, the cell loss probability of the queue B can be computed as: where pl is the load offered to the leaky bucket. The dimensioning problem requires to fix the values of the two design parameters a and so that conditions 1) and 2) of Sec. I11 are satisfied. The leaky rate a is easily computed by imposing: a SB,, (I +p) (18) Then the bucket size can be evaluated by imposing: B l a (19) from (16) and (17). it follows that the condition above is satisficd when: Therefore the bucket size is computed by solving the equation (13) iteratively and stopping the computations when the condition (20) is satisfied. As for the performance evaluation, the burst length is equal to the time required to fill in the bucket transmitting at the link rate. Since during this time interval the bucket is drained at the leaky rate a, the burst length is given by: - I -a By assuming the transmission ends when the bucket is full and resumes when it drops again to zero, the silence legth can be computed as - and a the burst period is given by: - + I-a a IV. NUERICAL RESULTS The two UPC mechanisms presented in the previous section have been dimensioned and compared for the three classes of CBR sources listed in section 11. The CDV affecting the cell stream has been evaluated by assuming a global offered load p = 0.9 on the access multiplexer. The target loss probability for conforming cells has been set equal to 10-9 and the computations have been performed by varying the allowed overload p from 0.01 up to The performance evaluation of both the mechanisms has bccn based on tho worst case traffic allowed to enter the nctwork; since in all the cases the pcak rate of such traffic is equal to the link rate, the only parameter taken into account has been the burst length. Its behaviour versus p is drawn in Fig. 8 for the jumping window mechanism and in Fig. 9 for the leaky bucket mcchanism. By looking at the graphics it is clear that for both the mechanisms the resulting burst length is very sensitive to p. as well as to the cell inter-arrival time d; more precisely, the lower p and d are, the longer the burst length results A.2.6

7 loo I \ 80 e gk3.i - c. L" 40 1 \d= d= Allowed overload 9% Fig. 8 Burst length versus allowed overload for the Jumping Window mechanism 30 I 25t increases. oreover, it is worth noting that the higher the connection bandwidth is, the greater p should be. A possible dimensioning of the two mechanism for the considered sources is reported in Table I (jumping window) and in Table I1 (leaky bucket). The leaky bucket comes out to have better performance than the jumping window, specially for high demanding conncctions. The outgoing burst length, in fact, is much lower for the leaky bucket than for the jumping window (50% for the low speed source, 33% for the medium speed one, 15% for the high speed one), and this leads not only to less critical worst case traffics, but also to shorter reaction times for non conforming sources. A further remarque is relevant to the dependence of the results on the amount of CDV affecting the monitored connection. It is obvious that the greater the CDV, the more critical the control is. As a consequence, the maximum CDV value at T reference point should be limited and, possibly, standardized, to help the dimensioning of the UPC mechanism. oreover, it is worth noting that a tight limitation of this value could be an effective way of improving the performances of any UPC mechanism. TABLE I Performances of the Jumping Window 5 I I I I Allowed overload 9% Fig. 9 Burst length versus allowed overload for the Leaky Bucket mechanism TABLE 11 Performances of the Leaky Bucket Aiming at optimizing thc network resources utilization, this behaviour should be carcfully evaluated; each connection, in fact, uses transmission resources in terms of bandwidth and buffer space: by reducing the allowed overload the required bandwidth is reduced at the expense of the buffer space. The optimum trade-off between these requirements may depends on many 'local' factors such as the amount of buflcr space available; but. in general, very little advantage can be reached by increasing the allowed overload beyond a certain lhreshold (dependent on the connection bandwidth), since the curves in Fig. 8 and 9 tcnd to be flat when p 6A

8 V. CONCLUSIONS The UPC function is a key issue for congestion control in AT networks and calls for urgent clarification in the standardization bodies. Focusing on the peak cell rate conuol, a key role in designing and evaluating a UPC algorithm is played by the CDV introduced inside any multiplexing equipment situated between the source and the UPC unit. In the paper the distribution of the CDV affecting a periodic sueam is evaluated by means of an analytical model. oreover, on the basis of the obtaincd distribution, the relevant parameters of two policing devices (the jumping window and the leaky bucket) are dimensioned and the two algorithms are compared on the basis of some proposed performance indcccs. The presented numerical results lead to the conclusions that the leaky bucket allow a tighter control, especially for high demanding sources. On the other hands, none of these two algorithms is able to control the peak rate on a very short time scale. In particular both of them allow short burst of cells to enter the network at the full link rate. As a consequence, the worst case traffic allowed to enter the network can be quite different from the expected one and this fact should be carefully taken into account in designing the call admission control procedure Lo guarantcc: an effective protection of the network against congestion. [lo] P. Castelli, E. Cavallero. A. Tonietti:" On the interexit time distribution of a constant bit rate Source in an AT ultiplex"; COST 224, TD(90)56, September 1990; [ll] Guillemin F.. Roberts J.W.: "Jitter and bandwidth enforcement"; COST 224 TD (91)OlS. April 1991; [ 121 Butto'.. Cavallero E., Tonietti A.: "Effectiveness of the Leaky Bucket policing mechanism in AT networks"; IEEE J. on Select.Areas Comm.. vol. 9. n. 3, April 1991; [13] Rathgeb E.R.: "The policing function in AT networks"; ISS '90, Stockholm, Sweden, June 1990; [ 141 Rathgeb E.R.: "odelling and performance comparison of policing mechanisms for AT networks."; IEEE Journal on Select. Areas of Comm., vo1.9. n.3. April 1991; [15] Turner J.: "New directions in communications (or which way in the information age?)"; Int. Zurich Seminar on Digital Comm.. Zurich, Switzerland. arch 1986; [16] CCITT SO XVIII Delayed Contribution 1021: "Cell transfer capacity parameters and their measurement"; Geneva, Switzerland. November 1990; References CCITT Rec :"Broadband Aspccts of ISDN"; atsuyama, Japan, December 1990; CCITT Rec : "B-ISDN General Network Aspects"; atsuyama. Japan, Decembcr 1990; Gallassi G.. Rigolio G.. Fraua L.: "AT: Bandwidth assignment and bandwidth enforcement policies"; Globecom '89. Dallas. Novcm. 1989; W. Kowalck. R. Lehnert: "The policing function to control user accessin AT nctworks: definition and implementation"; Proc. of ISSLS '88. Boston, USA, September 1988; P. Boyer:" A congestion control for AT"; Proc. of the 7th ITC Seminar, orristown. USA, October 1990; Dcnissen F., Desmet E., Yctit G.H.: "The policing function in an AT network"; 1990 Int. Zurich Sem.Digita1 Comm.. Zurich. arch 1990; Niestegge G.: 'The Leaky Bucket policing method in the AT network"; Intern. Journ. of Digital and Analog Comm. Syst.. v. 3, n. 2, June 1990; Guillemin F.. Boyer P.. Dupuis A., Komoeuf L.: "Peak rate enforcement in AT nctworks"; Submitted to INFWO '92. Florence, Italy. ay 1992; Roberts J.: "Jitter due to an AT multiplex. Application to Peak rate policing"; COST 224 TD(89)035. August 1989; A.2.8