attraction of ATM is its support for a number of di erent types of applications and ... the average bit rates over a long-term period is signi cantly smaller than their peak ... tra c envelope to assess if the available resource in the switch is su cient to ..... control measures are taken using CAC and UPC (Usage Parameter Control), ...
Call Admission Control Algorithms in ATM Networks: A Performance Comparison and Research Directions Mohammad A. Rahin and Mourad Kara
School of Computer Studies The University of Leeds Leeds LS2 9JT UK E-mail: {rahin, mourad}@scs.leeds.ac.uk Telephone: +44 113 233 6590 Fax: +44 113 233 5468 (Interim Research Report Draft 0.8 dt. 29.9.98)
Abstract
The aim of this paper is three fold: 1. to present an uptodate comprehensive review of connection admission control (CAC) algorithms, 2. to compare the performance of a mixed set of common and newer CAC algorithms and 3. to discuss reserach directions for CAC algorithms. We start by discussing connection admission control in ATM networks in terms of connection establishments and routing, the quality of service (QoS) parameters which de ne the CAC operation and a set of desirable properties. A comprehensive review of CAC algorithms then follow covering a wide range of dierent approaches, from mathematical/statistical, heuristic, measurement to arti cial intelligence methods. We also present a simple CAC performance framework discussing various performance metrics, analytical methods and performance assessment criterion. Quantitative performance comparison of a select six CAC algorithms are presented and their eectiveness in ATM networks under dierent operating conditions are discussed. Finally we discuss current research eorts to support CAC service. We argue that these research directions are essential for the development of CAC algorithms fully and implicitly supporting the QoS requirements of present and furute applications.
1 Introduction The Asynchronous Transfer Mode (ATM) is considered as the appropriate transmission technology for both local and wide area broadband communication networks (B-ISDN). The most important attraction of ATM is its support for a number of dierent types of applications and services with widely varying degrees of tra c characteristics and performance (QoS) requirements. ATM requires adequate and exible tra c control schemes to meet the QoS requirements of these services and applications. Call Admission Control (CAC) is the most important component in the tra c control framework proposed by ITU-T through Recommendation I.371[5] and ATM Forum UNI 3.0. [1]CAC is a sophisticated control mechanism whose speci c goal is to maintain a ne balance between the two contradictory objectives of maximising network utilisation and delivery of QoS (performance) guarantees to connections in progress. CAC is the rst control step in the provisioning of network resources to connections. It is basically a decision algorithm which on receipt of a new connection request determines whether or not to admit the connection based on the current usage level of network resources. The new connection is admitted only when there are su cient resources available to meet the QoS requirements of all the existing connections as well as the new connection. While CAC should seek to maximise the number of admitted connections it must not jeopardise/violate the performance guarantees to existing connections. Over the past years signi cant progress have been made in the theory and practice of ATM CAC. However, there are still some issues remain to be resolved. Full understanding of tra c characteristics and properties which is essential in exploiting statistical multiplexing in order to maximise the utilisation of ATM networks is to be made. Most of the present day CACs are based on complex queueing models and are known to have large processing demand. Alternative adaptive methods derived from Arti cial Intelligence (AI) can play an important role towards the development of fast intelligent CAC. These should be able to learn from the actual tra c behaviour to which they are subjected to and thus relieve the model-based dependency which otherwise aects queueing or stochastic theoretic solutions.
Development of a performance framework is also of paramount importance. This would allow comparison of various CAC approaches and solutions in a consistent and coherent manner. The performance framework would identify the necessary tools, metrics and methods for the appraisal of various CAC schemes. A benchmark suite for the testing of CAC performance under various trying scenarios is also required to test the robustness, exibility, e ciency and eectiveness of CAC schemes. The objective of this report is to gather thoughts towards the development of a such performance framework for CAC schemes. The report visits the subject of connection admission control in ATM networks from the perspective of performance requirements and presents a classi cation of a number of existing CAC schemes based on the methods employed. Brief discussion is made on how CAC performance is generally analysed and assessed. The report also reviews a number of key papers in order to identify the major on-going research eorts and future research directions.
2 Call Admission Control Provision of performance (QoS) guarantees to admitted connections at an ATM switch is made during the call set-up stage through the call admission control (CAC) scheme. Performance guarantees may be provided either in absolute (deterministic) terms or in statistical terms based on the QoS requirement of the call request and the nature of the connection making the call set-up request. In cases where deterministic performance guarantee is required by a call request, CAC base its decision on the maximum bit rate speci ed in the tra c descriptor of the call request in order to account for all congestion related eventualities. If su cient spare resource (bandwidth) is not available in the switch, the call request is rejected. otherwise the call is admitted. Deterministic allocation based on peak rate is very easy to accomplish and generally requires minimal processing. Deterministic allocation is best suited to constant bit rate (CBR) transmission such as uncompressed audio/video, low bandwidth telemetry etc. However, most present day applications fall into the category of variable bit rate (VBR) and as such, resource allocation based on their peak rate is liable to wasteage of valuable network resources. This is especially true for bursty multimedia applications such as compressed MPEG movies where the average bit rates over a long-term period is signi cantly smaller than their peak rates. Call admission criterion for a call request of a VBR connection based on a rate smaller than its peak rate but essentially greater than its average rate would signi cantly improve the utilisation of the network and reduce the wasteage of available bandwidth. This special bandwidth is often termed statistical bandwidth/eective bandwidth/equivalent bandwidth. CAC based on statistical bandwidth of VBR call requests form what it known as statistical allocation of resources and the process as statistical multiplexing. In statistical multiplexing the sum of peak rates of connections admitted onto a link can be greater than the link bandwidth, but this is allowed as long as the sum of their statistical bandwidth is less or equal to the link bandwidth. The performance guarantees provided to the connection admitted through statistical multiplexing however is of statistical nature, i.e. the QoS parameter bounds are speci ed in statistical terms; for instance, the probability that the transfer delay of a cell is smaller than given bound Dmust be greater than a given value Z . In [38] the authors exploited the intuitive property that over longer interval lengths, a VBR source such as MPEG may be bounded by a rate lower than its peak and closer to its long term average. The Deterministic Bounding Interval Dependent (D-BIND) tra c model is presented which employs tight analysis technique and explored the possibility of providing deterministic performance guarantees to VBR tra c while still achieving a reasonable network utilisation. The D-BIND model consists of a family of rate-interval pairs where the rate is a bounding rate over the interval length. The Hybrid Bounding Interval Dependent (H-BIND) model [39] is the later development of the D-BIND tra c model and captures the correlation structure and burstiness properties of a VBR stream. By exploiting the statistical properties of deterministically bounded stream it achieves statistical multiplexing gain. Krunz and Tripathi [41] also exploited the temporal structure of MPEG video sources to propose a scheme based on the eective bandwidth specifically tailored to MPEG video tra c to achieve stringent deterministic QoS guarantees through statistical multiplexing. The video sources are modelled using a tra c envelope that provides a deterministic time-varying bound on their bit rates. Scheduling schemes for both homogeneous and heterogeneous video streams has also been proposed in order to signi cantly reduce the eective bandwidth requirement.
1. Can you support a new connection with the given characteristics & QoS.
3. Yes, I can/ no, I can not.
2. Do I have sufficient resource? Will this connection affect the the existing connections?
Figure 1: Connection admission control
2.1 Call Set-up and Routing
For either the deterministic or statistical multiplexing the CAC decision process must address the following two issues: 1. The QoS requirements of the new connection must be guaranteed. 2. The QoS provided to existing connections must not be degraded to unacceptable levels when they multiplexed with the new connection. Within ATM networks, CAC is a local switch/node function, and is dependent on the architecture of the switch and local decisions and considerations on the strictness of QoS guarantees. However, the ATM VC routing protocol must ensure that a call request is routed along a path that leads to the destination and has a high probability of meeting the QoS requested in the call set-up. In other words it is expected that the switches traversed in the path will not reject the call. Each switch in path will execute its own CAC in turn and thus will for the overall call admission decision on the call set-up request from the source. In [19] a generalised scheme for call set-up procedure has been proposed where the call set-up process is accomplished in one round-trip time between the source and the destination. The destination host is the last point along the path where the acceptance/rejection decision for a call set-up request can be made. When a switch is revisited by a call set-up message during this messages's return trip, the resources previously reserved there must either be committed or released; hence a nal irreversible decision must have already been made. When a switch receives a call set-up message, either two or all three of the following tests are executed: 1. the deterministic test : Only if the new connection is deterministic and involves other existing deterministic connection passign through the switch. The deterministic test use worst-case tra c envelope to assess if the available resource in the switch is su cient to admit the new connection. 2. the statistical test : For both deterministic and statistical connection this test is required only if at least one statistical connection already passing through the switch or is to be set-up. This test involves all existing deterministic and statistical connections passing through the switch. The statistical test has two goals : (i) to determine whether for each statistical connection j passing through the switch nthe probability of a QoS parameter such as delay is higher than its bound d is below its maximum tolerable value, 1 ? z . (ii) for a new statistical connection i, to enable the destination host with su cient information in order to compute z . 3. the QoS bound test : Is required in all cases. If this test becomes successful, follow-up computation of the minimum feasible QoS bound for the new connection is necessary. j;n
j;n
i;n
2. CAC fails
Receiving host
1. GCAC suggests path
Sending host
3. Crankback
Figure 2: The crankback operation The tests to be done on each switch in the path assess the availability of su cient bandwidth in the links, processing power and buer space in the switch. Essentially, these determines whether or not the new connection may be admitted through the switch without adversely aecting the QoS guarantees to the connections already passing through the switch. If any test fails at a switch, the connection can not be set up along that route; the message is sent back, either to the source (which may then try alternate route or decide to wait) or to an intermediate switch that can try sending the message along another path. If all tests succeed, a reply message is sent back to the source for call set-up to be executed in each node along the connection's route and in the destination host. The Private Network-to-Network Interface (P-NNI) [2] and the Interim Inter-Switch Signalling Protocol (IISP) [4] speci cations of the ATM Forum de nes the mechanisms for routing and signalling connection requests within private ATM networks. P-NNI uses a source-based hierarchical approach for routing connection requests, in which end systems use periodically broadcast, aggregated topology-state information using P-NNI topology state packets (PTSP) to determine a tentative route along which a connection request is to be forwarded. Ideally, intermediate nodes should only need to perform CAC before forwarding the requests. Topology aggregation is needed to prevent a state explosion situation. Aggregation is a lossy process and usually leads to inaccuracies [6]. Since, CAC is a local matter concerning a node/switch, the actual CAC algorithm performed by a given node/switch is both system dependent and open to vendor dierentiation. This is tackled by de ning a Generic CAC (GCAC) algorithm. This is a standard function that any node/switch can use to estimate the expected CAC behaviour of another node/switch, using the QoS requirement of the new connection and that node/switch's advertised additive link metrics comprising of maximum cell transfer delay (MCTD) of a tra c class, maximum cell delay variation (MDV) of a tra c class, maximum cell loss ratio (MCLR) for CBR/VBR tra c classes, a desirability weight setby network administrator. A new connection request which is admitted by the CAC of a node/switch undergoes additional GCAC speci c tests in order to nd an acceptable path to the destination. Each node/switch in the path must still perform its own CAC on the routed request as the original state information encapsulated within the PTSPs is likely to change. Also, its own CAC is likely to be more accurate compared to the GCAC. Hence, disregarding the role of GCAC, there is always a possibility that a connection request may fail CAC at some intermediate node/switch. A technique known as cranckback (Fig. 2) is speci ed within P-NNI which attempts to recover from a CAC failure from a GCAC suggested route. Crankback is where a connection which is blocked along a selected path is rolled back to intermediate node, earlier in the path. Attempt is then made to nd a new path to the nal destination from this intermediate node. Similar procedure as before is used, but this time a newer and likely to be more accurate set of information is available at disposal.
2.2 Multiplexing Gain and CAC
The advantage of CAC based on the peak rate bandwidth allocation is that it is easy to decide whether to accept a new connection. This is due to the simple requirement that only knowledge of
the peak rate of the new connection is known and the new connection is accepted if the sum of the peak rates of all the existing connections including the new connection is less than the capacity of the link. However, the main disadvantage of peak rate allocation is that unless connections transmit at peak rates, the link capacity will be severely under-utilised. The statistical multiplexing method seek to improve the utilisation of the link capacity by admitting new VBR connections based on their statistical/eective bandwidth. This allows admitting more connections than otherwise possible. The advantage of using statistical multiplexing over deterministic multiplexing (peak rate allocation) is expressed using the metric multiplexing gain and is de ned as the ratio of peak cell rate with respect to eective bandwidth. Extension can be made to de ne network multiplexing gain as the mean value of multiplexing gains of individual connections. So, if there are N connections in the network which have multiplexing gains g1; g2 ; ::::::; g respectively, then the network multiplexing gain g may be calculated as, g = (g1 + g2 + ::::: + g ) N
N
N
The above is the representation of network multiplexing gain in very simple form. For a homogeneous case with N connections of identical peak rate R the multiplexing gain g may also be expressed as: g = N:R C ; where C is the exact link bandwidth needed to meet the QoS requirement of all N connections. The representations above does not consider the connection durations and their absolute bandwidth requirements. A more advanced formula for network multiplexing gain according to [10] is :
:::::: + p T ) ; g = ((ep1TT1 ++ ep2TT2 ++ ::::::: +e T ) 1 1 2 2 N
N
N
N
where p , e , T are peak cell rate, mean values of required resource and connection duration of the i-th connection, respectively, i = 1; 2; :::::; N . For VBR connections the required resource is the i
i
i
eective bandwidth of the connection.
2.3 Statistical Multiplexing and CAC Algorithms
Statistical multiplexing makes good economic sense while dealing with bursty tra c. As opposed to peak rate allocation as in deterministic multiplexing, in statistical multiplexing allocation based on the eective bandwidths of connections are used. This lead to improved uitlisation of network resource as the eective bandwidth for most VBR tra c is signi cantly smaller than their peak rate. However, eective implementation of statistical multiplexing is di cult [50]. Di culties arising from the characterisation of the arrival process and lack of detailed understanding of how an arrival process is shaped within a ATM switch is one of the most important hindrance to the developments of e cient and eective statistical multiplexing CAC. The other major problem in statistical multiplexing stems from the real-time constraints. An admission decision must be made as quickly as possible almost on the y. This implies that the processing should not be CPU intensive. However, most statistical multiplexing problems are often formulated as queueing problems [7][54][26], solutions to which are often very complex and CPU intensive [8][15]. The most important challenge towards developing an e cient and eective CAC algorithm is how to determine the bandwidth requirement of a connection request of uctuating bit rate su ciently quickly? For CBR connections , this is fairly trivial and is not considered any more in this report. However, for VBR connections this is still an open problem and a multitude of dierent CAC approaches have been proposed in the literature. An ideal CAC scheme should aim to possess the following characteristics [8][42] :
Simple : The algorithms must be simple in terms of economic implementability and also fast. Flexible : The algorithmic architecture should have su cient adaptability to meet the needs of new services expected to appear in future. Robust : The algorithms must be able to operate eectively even when some of the assumptions do not hold or only partially hold.
Calls
Bursts
Cells
Figure 3: Time scale hierarchy in ATM tra c
Fast : The algorithm must be fast enough to compute admission decisions within real-time
constraints. E cient : The algorithm should achieve high resource utilisation through maximising the exploitation of statistical multiplexing. Eective : Must be able to guarantee the QoS promised to the end user. Controllable : Tra c control must be achieved without degrading the network performance.
In ATM networks QoS requirements must be met end-to-end. However, as mentioned earlier the call set-up and routing procedures assume CAC as a local node/switch matter. This may be realised by decomposing the network as a set of single queues, one for each link. Analysis of the CAC procedure can then be performed on individual single queues to analyse the end-to-end performance guarantees. The single queue representation of individual links in the ATM network assume that the arrival process at intermediate node is the same as at the source. In practice this does not always hold. However, in [17] it is shown that, if the peak bit rate is a small fraction of the link capacity the eect of buering and multiplexing at a node on the tra c characteristics is negligible. This suggest that the single queue representation of a link in ATM networks may be accepted in many cases. Analysis of statistical multiplexing may be done at three dierent levels (Fig. 3), the call level, the burst level and the cell level [32]. These three levels are dierentiated with the scale of time being used. The call level analysis consider connection set-up and clear events delimiting the connection duration which is typically in the range of couple of minutes. The call level analysis explore statistical multiplexing CAC in terms of call blocking probabilities, set-up and routing behaviours. Burst scale analysis addresses the behaviour of a transmitting connection, characterised as a cell ow rate over an interval during which the rate is assumed constant. The duration usually considered is in milliseconds. On the other hand cell scale analysis investigates at a more minute level, i.e., the behaviour of cell generation/loss/queueing and concerns with the time interval between succeeding cells in microseconds durations. For practical considerations, some form of structuring is generally required while allocating resources within a ATM switch. One such structuring method is the service separation procedure which divides the connections into a set of service classes. The members of a particular class are similar as regards to their statistical tra c characteristics and/or performance requirements. Bandwidth can then be allocated according to the nature and needs of the service classes. This way statistical multiplexing can be contained within each class and reasonable QoS performance guarantees can be provided to dierent service classes with widely varying performance requirements. A number of studies [33][28][9] on resource management for ATM networks have adopted the service separation technique in various forms. Performance system models for both call and burst/cell levels can be made around the service separation principle. Another parameter which has a profound eect on the performance analysis of the queueing behaviour of an ATM multiplexer is that of the size of the buers located in the multiplexer. Large buers prevent degradation of CLR by holding over ow cells, but in doing so they may introduce
long delays which are undesirable for time-sensitive tra c. Two dierent buer related behaviour may be analysed - the cell scale buer class and the burst scale buer class depending on the size of the buer used [49]. Cell scale buers consider the congestion at the cell level, i.e. simultaneous cell arrivals from multiple sources. On the other hand burst scale buers store the excess rate tra c in cases where the arrival rate exceeds the link capacity. Two dierent framework may be identi ed - (a ) the burst loss framework for cases where the system is either without buers or with only small buers and burst scale congestion result in cell loss and (b ) congestion is handled using larger sized buers in burst delay framework where delay in introduced as by-product.
3 QoS Requirements and Service Classes When the call set-up request of a connection is accepted it is said that a contract is made between the tra c user and the ATM network. The ATM network oer a speci c set of service classes, and the connection source must specify a desired service class for the connection at the time of making the call set-up request. Service classes are used by ATM networks to dierentiate between speci c types of connections, each with a particular mix of tra c and QoS parameters. The set of service classes based on QoS parameters and as de ned in ATM UNI 4.0[3] are as follows :
Continuous Bit Rate (CBR) : End systems would use the CBR service class to carry constant
bit rate tra c with a xed timing relationship between data samples, typically for emulating circuit switching. Real-time applications with xed bandwidth such as telephone, radio, TV or low bandwidth telemetry may use CBR. Variable Bit Rate - Real Time (rt-VBR) : The rt-VBR service class is used connections that carry variable bit rate tra c in which there is a xed timing relationship between samples. Delay sensitive applications such as interactive video compression fall into this category. Variable Bit Rate - Non-Real Time (nrt-VBR) : The nrt-VBR service class is used for connections that carry variable bit rate tra c but without any timing relationship between data samples. However, a guarantee of QoS is still required. Multimedia electronic email and other non delay-sensitive application fall into the category of nrt-VBR. Statistical multiplexing is well exploited in both categories of VBR tra c. Available Bit Rate (ABR) : As with the nrt-VBR service, ABR supports variable data rate transmission and does not preserve any timing relationship between source and destination. Unlike the nrt-VBR service, however, the ABR service does not provide any guaranteed bandwidth the user. Instead, the network provides best eort service, in which closedloop feedback is used to increase the bandwidth available to the user - the Allowed Cell Rate (ACR) - if the absence of congestion and to reduce the bandwidth where is congestion. Through such ow control mechanisms, the network can control the amount of tra c that can be injected into the network and minimise congestion induced cell loss within the network. It is however, also possible to provide a guaranteed Minimum Cell Rate (MCR) for an ABR connection. Unlike the CBR and both forms of VBR service classes where preventive control measures are taken using CAC and UPC (Usage Parameter Control), ABR control mechanism is essentially of reactive type. Unspeci ed Bit Rate (UBR) : The UBR service does not provide any performance guarantees. The user may send as much data up to a speci ed maximum as it likes while the network makes no guarantees whatsoever on the cell loss rate, delay or delay variation that might result. The UBR service is best suited for delay-tolerant low priority applications such as background le transfers. Both ABR and UBR make use of left-over bandwidth available to the ATM network.
The ITU-T have also de ned a set of four ATM Transfer Capabilities (ATCs). An ATC is a medium of speci cation of a service model composed of tra c characteristics and QoS requirements. Of the four ATCs, three match very closely with three of the four ATM Forum service classes. The other one, ATM Block Transfer (ABT) is a altogether dierent service model. Of the ATM Forum service classes, UBR is not represented within ITU-T ATCs. The four ATCs de ned in ITU-T Recommendation I.371[5] are :
Deterministic Bit Rate (DBR) capability : This is similar to CBR class, but may also be
used to connection types other than CBR. The connection does not have to transmit at the negotiated PCR. Statistical Bit Rate (SBR) capability : This corresponds to the VBR class de ned by ATM Forum. SBR also supports renegotiation of performance guarantees using modi ed tra c descriptors over a number of phases, where a phase is de ned as the time interval during which the tra c descriptor does not change. From practical considerations it is su cient to assume that the network allocates bandwidth according to the declared SCR for each phase of the connection. Available Bit Rate (ABR) capability : This also corresponds with the ATM Forum ABR service class. ATM Block Transfer (ABT) capability : The user de nes a block structure in its data stream. For each block, a constant bit rate (up to the PCR) is negotiated between the user and the network by the use of Resource Management (RM) cells.
During call set-up the connection source informs the network about the type of service required, the tra c parameters of the data ows in each direction and QoS requested for each direction. Together, these form the tra c descriptors of the connection. Tra c sent along connections of any type are de ned by a set of tra c parameters :
Peak Cell Rate (PCR) Cell Delay Variation Tolerance (CDVT) Sustainable Cell Rate (SCR) Burst Tolerance (BT) Minimum Cell Rate (MCR) for ABR only
These parameters above together form a QoS envelope around a tra c stream. However, not all of these parameters are required for all service classes. For example, CBR connections only need to specify PCR (the frequency at which data samples are pushed out) and CDVT (the limit on the transfer delay variation). VBR connections on the other hand require additional parameters such SCR and BT to specify the long term mean cell rate and the size of the maximum burst of contiguous cells that can be generated. ABR service request should specify both PCR and MCR so that the dynamically controlled ACR hovers between PCR and MCR. The current set of QoS parameters consist of three delay parameters and one dependability parameter. The three delay parameters are :
Peak-to-peak Cell Delay Variation (CDV) Maximum Cell Transfer Delay (Max CDT) Mean Cell Transfer Delay (Min CDT) The dependability parameter is :
Cell Loss Ratio (CLR) The call setup procedure (UNI 4.0 & P-NNI) will treat the rst three parameters as dynamic, additive metrics and will accumulate their values through the network in signalling and routing requests. On the other hand, the CAC algorithms implemented at local links/nodes will seek to provide the QoS guarantee on the dependability parameter, CLR. The ATM Forum and ITU-T classi cation of service class in terms of QoS requirements is from the view point of the provisioning of end-to-end performance (QoS) guarantees through the network. Classi cation of service classes may also be made from the view point of the operation of a local CAC algorithms. In [42] QoS classes are de ned as follows :
Class 1 : with stringent CLR (Cell Loss Ratio) and CDV (Cell Delay Variation) requirement;
Class 2 : with stringent CLR requirements, but no need for CDV guarantees; Class U : with no need for guarantees on either CLR or CDV. Class 1 and Class 2 services may be mapped to either CBR and VBR connection requests depending on their QoS requirements. On the other hand, Class U may be used for ABR and UBR connections. A very simple CAC algorithm can then be speci ed as follows :
Class 1 and Class 2 connections are accepted if : X
PCR +
X
c1
MfCR C
c2
where C is the link capacity, PCR is the connection peak cell rate, and is a protection coe cient ( 1) which can be used to set aside some leftover bandwidth available to Class U connections. MfCR is the Modi ed Cell Rate, and is a parameter characterising connection with a cell rate value midway between the PCR and SCR (Sustainable Cell Rate), using a linear modi cation factor such that MfCR = SCR + (PCR ? SCR). Class U connections are accepted if : X
PCR C ?
cU
X
PCR ?
CBR
X
SCR
!
V BR
where is the bandwidth utilisation coe cient, likely to be greater than 1, which may be used to dimension the leftover bandwidth that can be allocated to Class U connections. In the simple CAC algorithm presented [42] and are parameters of the algorithms, whereas is used to hold the notion of burstiness of connections. Also, MfCR should not be regarded as the eective bandwidth as de ned in [26] since this simple CAC algorithm does not address any QoS requirements (CLR, CDV) of call set-up requests.
4 CAC Algorithms CAC for VBR tra c utilising the principle of statistical multiplexing have been studied extensively in the literature. A number of dierent approaches have been used. Some of these approaches are model based, meaning an explicit model of tra c is required. Others use only a subset of the available tra c parameters such peak rate, mean rate etc. The main component of a CAC algorithm is the estimation of bandwidth required by a set of connections such that QoS requirement of each of the connections can be satis ed. In other words, the problem can be stated as, for N multiplexed connections the determination of total required bandwidth C such that the probability that the total instantaneous aggregate bit rate exceeds C is less than a given value . If r (t) is the instantaneous bit rate of connection i, the total bandwidth requirement is the minimum value of C such that, i
Pr
"
X N
!
#
r (t) C < i
i=1
Among the various CAC approaches reported in the literature, we present below a selected few The discussion on each of these approaches centre around their formulations, basic assumptions, salient features and their shortcomings. It is hoped that by reviewing these, directions and scope for future research for the design of eective CAC algorithms and their performance assessment will emerge. A more complete and detailed review on CAC algorithms may be obtained from [50].
4.1 Gaussian Approximation Method
The Gaussian approximation method is a simple and fast scheme for the determination of bandwidth requirement. The central limit theorem which states that with the number of connections approaching in nity and that no single connection is dominant, the Gaussian distribution approximates the distrbution of aggragate tra c is the basis for this scheme. The mean rate and the standard deviation of its bit rate are the characterising P feature of each connection i. For large number N of connections, the mean arrival rate = = and the variance of arrival rate 2 = P =1 2 follows from the Gaussian approximation. However, for small N the above is not valid and the bandwidth required estimated this way may be too conservative. Analysis of the Gaussian approximation lead to the estimation of buer over ow probability as [27], ! # " X ?C r (t) C = p1 e? Pr(overflow) = Pr 2 =1 and the upper bound to cell loss probability as [50], i
i
N i
N i
i
i
i
N
(
i
2 2
)2
i
Pr(loss) =
E
hP
N i=1
r (t) ? C
+
i
?C p e? 2 (
2 2
)2
where r (t) is the instantaneous bit rate of connection i. The Gaussian approximation method is an appealing scheme because of its simplicity. However, this simplicity also works against it in the way that the approximation is only valid for large number of connections. In cases where this assumption no longer hold, the scheme is not accurate being too conservative and at the same time optimistic. Also, all connections are treated equally in terms of cell loss requirements and the model is based on a buerless system. As a result, the scheme fail to fully exploit statistical gain. i
4.2 Convolution Method
The convolution algorithm is also based on buerless queuing model and found to be very accurate. A simple burst tra c model comprising of peak rate R and mean rate r is used. No burst length parameter is required. The probabilities that a connection is in burst state is r=R and is in idle state is 1 ? r=R respectively. The connection holding time distribution is assumed arbitrary. Each connection is modelled using a continuous ow approximation ( uid ow model). The total required bandwidth requirement is calculated by convoluting the bit rate distribution of each connection. The method also allows accurate estimation of cell loss. However, the computation requirement grows very quickly with increasing number of connections and soon may grow to such an extent to unable to meet the real-time requirement of CAC. Approximations based on boundary value may be used to overcome this de ciency.
4.3 Eective Bandwidth
The eective bandwidth method [26][31] determines a bandwidth which is midway between the peak and mean rates of the connections similar to the two methods above. The essential dierence, however, is that the eective bandwidth thus computed will be able to support the cell loss rate bound speci ed for individual connections. Also, the method considers the eect of buering. With a large buer assumption, the loss rate can be approximated by an exponential function of the buer size. The loss rate is approximately ef? ( )g, where B is the buer size and I (C ) is some increasing function of the buer service rate C and tra c statistics. I (C ) can be substituted by and may be used as a measure of the upper bound of the cell loss rate. For the CAC function at a ATM multiplexer, we can then state lim 1 log P (W B ) ; BI C
B
!1 B
where W is the stationary buer occupancy. It is shown in [36][37] that under suitable assumptions the above constraint can be satis ed when X N
c ( ) C ; i
i=1
i
where C is the total capacity of the link capacity of the multiplexer and c ( ) is the eective bandwidth of the connection i corresponding to it's cell loss upper bound . The eective bandwidth is between the peak and mean rates of the connection and the dierence between peak rate and c ( ) is the bandwidth saving through multiplexing. The eective bandwidth of a single source may be derived using the interrupted (ON-OFF) uid ow model, where each source is characterised by its peak rate R, activity ratio (i.e, the fraction of time the source is active) and the mean duration of the active period b. We also assume a nite buer of size B and constant service time. The eective bandwidth c corresponding to a given cell loss upper bound can then be derived using the technique suggested in [7] as, i
i
i
i
i
= exp ? b (1B?(c ?)(R R?)c) c ;
where
= (c ? cR(1) ?+ ) (cR ? c) :
The eective bandwidth c can now be solved from the above expression for . However, it can only be solved numerically and at considerable computational eort. An approximation solution based on b = 1(typically < 1) is, p
2 c = R a ? B + (a2?a B ) + 4a B ;
where
a = ln 1 b(1 ? )R:
The resulting eective bandwidth may however be inaccurate and highly conservative when buers are small or of moderate size[27][53]. The eective bandwidth estimated under small buer condition has been found to be signi cantly higher than the ones measured through simulation. This reason for this discrepancy is due to the fact that the eective bandwidth formulation is made under the asymptotic assumption that the product of buer size and cell loss rate tends to be zero and that it uses the buer over ow probability as the QoS requirement. A practical solution [27] which addresses the e ciency of eective bandwidth approach and also aim to improve the utilisation of multiplexing gain is based on two dierent, but complimentary approximations. The rst approximation assumes a uid- ow model similar to the eective bandwidth approach which ignores the eect of multiplexing gain between dierent sources and as a result may overestimate the required bandwidth requirement. The second approximation is that of Gaussian approximation which result in a bandwidth requirement under usual assumptions (buerless model and large N ). The suggested required bandwidth is given by the formula minfC ; C g: g
e
C is the total required bandwidth derived using the Gaussian approximation, g
C =
X N
+ i
g
p
?2 ln() ? ln(2)
X N
!
; i
i=1
i=1
where is the mean arrival rate and is its standard deviation for each connection. C is the total eective bandwidth requirement, i
i
e
C =
X N
c: i
e
i=1
Other suggestions to overcome the shortcomings and improve the accuracy of eective bandwidth method include combining the Cherno bounds and the eective bandwidth approximation [16], on-line evaluation of eective bandwidth utilising maximum entropy as a method for characterising tra c sources and their eective bandwidth [56].
Burst Admission Decision
Burst Controller
Buffer Occupancy Information
Frre Buufer Information
SOURCE NETWORK
Ri Buffer Discarded Burst
Figure 4: The fast buer reservation scheme
4.4 Diusion Based Method
In this approach [22] diusion processes with absorbing boundaries and jumps are introduced as more accurate continuous approximations of discrete queuing system for light and heavy tra c. This contrasts with the classical models in which re ecting boundaries are used and lead to a computationally very e cient and easily implementable CAC algorithm. The diusion based CAC procedure is based on two statistical bandwidth formulae for the required bandwidth. These are denoted as C 1 and C 2 and de ned as the statistical bandwidths obtained from the diusion model of a nite and in nite capacity queuing system respectively using the the instantaneous return process. These two statistical bandwidths are expressed as, df
C and similarly, where
df
p
df 1
C
= ? + 2 ? 22 !1 ; p
df 2
= ? + 2 ? 22 !2 ; p !1 = ln 2 ;
p !2 = ln 2 ? ln() ;
= 2B 2 :
In the above expressions, is the maximum acceptable cell loss ratio, is the aggregate cell arrival rate, 2 is its instantaneous variance, is the cell arrival process instantaneous variance, B is the buer size. The two statistical bandwidths capture the interaction between individual tra c streams at the ATM multiplexer using the users' cell loss requirements, their aggregate tra c characteristics, and the available buer size at the multiplexer. They also de ne the admissible range for various classes of connections based on their tra c descriptors for both small scale and large scale buer conditions. Comparison with other methods such as Gaussian approximation and eective bandwidth revealed that the diusion based approach is conservative with respect to cell loss, but more economical in bandwidth allocation and thus lead to larger admission regions for both homogeneous and heterogeneous tra c [23]. Also, the increase in required bandwidth with increasing number of connection is less than linear as compared to the eective method where the increase is linear.
4.5 Fast Buer Reservation Method
The fast buer reservation method [55] is an open loop scheme to prevent a ATM switch from tra c overload by a bandwidth reservation mechanism at the burst level. The ultimate aim is to
preserve the integrity of the bursts as a whole. The admission control is implemented at burst level rather than at the call level in contrast to other methods. Each virtual circuit passing through the switch is modelled as a two-state machine which can be either in active or idle. The source is expected to transmit at its peak rate when in active state and accordingly a prespeci ed number of buer slots appropriate to its peak rate is allocated to an active VC. Access to this allocated buer slots is then guaranteed until the VC returns to idle state. Transition between the two states occur with the receipt of specially marked start and end of burst marker cells. Within a burst, the well-behaved cells which use the reserved buer slots leave unmarked, while the misbehaved cells which use the unreserved buer slots are marked. If there are insu cient free buer slots to hold the bursts when a new start-of-burst cell arrives, the entire burst is discarded immediately. The burst admission controller maintains a database of VC status comprised of occupied buer information, free buer information and states of individual VCs. The maximum number of buers in cell slots B for a given circuit i in active state is given by, i
B :R B = C ; sl
i
i
where C is the link rate, B is the number of buer slots available and R is the peak rate of the i-th VC. If there are N VCs of dierent classes with instantaneous buer demands x1 ; x2 ::::::; x , the total buer requirement can be determined from the simple summation of all the individual buer demands such that the following performance criterion is satis ed. sl
i
;
X N
N
x :c C ; i
i
i=1
where c is the eective bandwidth for the discrete time ON-OFF tra c source for the given VC
i.
i
Enhancement to the fast buer reservation method has been proposed in [8] which seek to improve the buer utilisation and statistical gain by modifying the buer allocation rule taking into consideration the bursty nature of the tra c.
4.6 Measurement Method
The various CAC approaches described above are based on parametric models of tra c. In other words certain tra c source model, in particular, the ON-OFF source model is used. The ONOFF model is particularly suitable as it usually do not underestimate the cell loss and essentially encapsulates the behaviour of worst case tra c characteristics. However, because of the mathematical and computational complexities, often a number of assumptions derived from experience or practical considerations are made. These assumptions may not always hold under all tra c conditions. Also, the application making the call request may not be always able to correctly characterise before any tra c is transmitted. The measurement method [12][25][40][43] attempts to measure the bandwidth requirements directly. This avoids the problem of requiring new call request to specify a parametrised tra c model in advance and removes the estimation of redundant information. The measurement method relies on on-line measurement of tra c owing through a switch and requires very little declared information from a new call request, often only specifying the peak rate is necessary. However, additional information from the call request may be used to improve the required bandwidth estimation procedure and thereby the e ciency of the CAC process. An initial estimate of the bandwidth requirement may be made from the available parameters if available. This estimate is then re ned through on-line measurement. In the absence of additional parameters, a more conservative estimate may still be made from the declared peak-rate. The on-line measurements suer from the fact that the bandwidth that a connection requires uctuates over time. Accordingly, it takes time to have a reasonable estimate of this bandwidth. The on-line measurement of average bandwidth being used should incorporate a notion of history so as to cater for long-range dependence of the aggregate tra c. To calculate the average aggregate arrival rate from a measured arrival rate r at the i-th measurement interval the exponentialweighted moving averaging technique with a weight w may be employed, avg = (1 ? w) avg + w r . The time constant for this is, t = ?1= ln(1 ? w) A, where A is the length of each measurement interval. The time constant t should be as long as the interval from when a connection is admitted, until the measurements are likely to actually re ect tra c from that connection [20]. If it is i
i
CAC
CAC Idle
Call Request
Release Call
C + p e n+i
