Barria, JA

Salles, RM

IEEE Communications Letters

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320 IEEE COMMUNICATIONS LETTERS, VOL. 8, NO. 5, MAY 2004Proportional Differentiated Admission ControlRonaldo M. Salles, Student Member, IEEE, and Javier A. Barria, Member, IEEEAbstract—This letter presents a new admission control policyinspired in the framework of proportional differentiated services(PDS). While most of previous PDS has focused on averagequeueing delays and packet drops to differentiate the perfor-mance of adaptive applications, the proportional differentiationadmission control (PDAC) differentiates inelastic traffic in termsof blocking probabilities. The PDAC is built up using asymptoticapproximation theory, employs a class based approach, andconforms with the PDS requirements of predictability and control-lability. Numerical experiments confirm a good performance ofthe approach.Index Terms—Admission control, asymptotic approximation,proportional differentiated services.I. INTRODUCTIONADMISSION control is fundamental for the adequatesupport of inelastic traffic in data networks. This type oftraffic is characterized by stringent quality of service (QoS)requirements and usually do not adapt to network congestionsignals (e.g., real-time traffic). Regarding IP networks, theIETF IntServ and DiffServ architectures have emerged as themost prominent proposals to attend the QoS requirementsposed by current network applications. However, while the firstone may suffer from scalability problems, the latter may onlyprovide qualitative assurances and lacks control to the networkoperator. Recently, a scalable, predictable (differentiation isindependent of class load variations), and controllable (networkoperator should be able to adjust the relative QoS betweenclasses) service architecture, the proportional differentiatedservices (PDS) [1], has been proposed as an alternative toovercome those problems.Most PDS implementations do not employ admission controlor resource reservation and so they do not serve for inelastictraffic. However a QoS network offering PDS may be also re-quired to transmit inelastic traffic. The proportional differenti-ated admission control (PDAC) bridges that gap and brings thePDS framework to the context of inelastic traffic. It provides apredictable and controllable network service for inelastic trafficin terms of blocking probability, and uses a PDS equality to de-fine such service.Manuscript received September 18, 2003. The associate editor coordinatingthe review of this letter and approving it for publication was Prof. M. Devetsiki-otis. The work of R. M. Salles was supported by the CNPq, Brazilian Govern-ment, under Grant 200049/99-2.The authors are with the Department of Electrical and Electronic En-gineering, Imperial College London, London SW7 2BT, U.K. (e-mail:r.salles@imperial.ac.uk; j.barria@imperial.ac.uk).Digital Object Identifier 10.1109/LCOMM.2004.827384II. THE PROPORTIONAL DIFFENTIATION ADMISSION CONTROL(PDAC)A. Environment and FormulationWe consider a heterogeneous system where each connectionhas an associated bandwidth requirement that should be guar-anteed end-to-end throughout its lifetime. To facilitate scala-bility, connections are grouped into classes that differ accordingto . A connection should use class if , and is thenearest to among all classes. Same class connections are ag-gregated into path flows so that they can be managed as a singleentity inside the network The aggregate requirement of classflow is then , where is the number of class connec-tions. A simple admission test can be usedto control the access to class partition . This class-based ap-proach is conservative since we assumed traffic to be inelasticand provided in an all-or-nothing basis. Signalling is manda-tory, however, as long as we are conservative (i.e., use as thepeak rate) per-flow management is reduced. There will be noneed to allocate resources per-flow since class partition is likelyto be over provisioned. Moreover, there will be no wasted re-sources given that all available resources can be used by otherunderlying PDS or best-effort traffic.The above characterization is fundamentally different fromthe adaptive traffic commonly assumed in PDS. In our case,the only way to regulate the aggregated class flow and stillmeet bandwidth requirements is through blocking. Note alsothat blocking is a QoS parameter relevant for inelastic traffic.Each class incurs a certain blocking probability and ac-cording to proportional differentiation goal, PDAC is defined as(1)where, is the weight of class . The weights work as prioritiesassigned to the classes, the larger the weight the higher the ad-mittance priority. The strategy ensures a flexible traffic controlfor the network operator (controllability). The problem is thento find a resource allocation mechanism for the link capacitywhich guarantees (1).The system can be modeled as a stochastic knapsack [2] ofcapacity , which under a complete partitioning scheme (CP)is reduced to independent Erlang subsystems (exponentialarrivals and general session holding times). Each class has anallotted partition and offered load . The PDAC problemunder CP is thenfind (2)s.t. (3)(4)1089-7798/04$20.00 © 2004 IEEESALLES AND BARRIA: PROPORTIONAL DIFFERENTIATED ADMISSION CONTROL 321where , andare given. The above problem is a huge com-binatorial problem even for small instances. Moreover, it is notlikely to have a feasible solution given the hard equality con-straints on (3). Therefore we work on two different directions:find ways to reduce the complexity of the problem and relaxPDAC definition in order to avoid sharp equality constraints.B. Asymptotic ApproximationFrom the early studies on the Erlang B formulae [3], ,it can be shown that blocking probability in the limiting regime(when and ) takes the following form:(5)where . This result simply states that expressions canbe strongly simplified when the capacity of links and offeredloads are increased together: and .The condition can be satisfied in links used by a large numberof flows, where each class partition is kept below .Using asymptotic approximation, (3) becomes(6)Taking the class of minimum weight as reference, thepartitions that satisfy PDAC goal can be now obtained from,(7)(8)Although the approximation allowed a significant reductionin the complexity of the PDAC problem, the feasibility issue stillremains. For instance, to guarantee(9)Therefore, given the capacity of the link , it is not alwayspossible to solve the PDAC for general values of , andeven when considering the asymptotic approximation. Thesharp equality constraints in the PDAC definition need to be re-laxed.C. Problem RelaxationIn addition to the asymptotic approximation, we relax thePDAC definition in order to avoid the equality in (1) and over-come the feasibility difficulty. To achieve that the op-erator is employed redefining the service goal, or in other wordsdefining the RPDAC (Relaxed PDAC) problem(10)(11)(12)The rationale behind the operator is that while it triesto minimize the differences between of the classes, it doesnot impose strict equality.With the introduction of an extra variable , thein (11) can also be written as:(13)Since there is no restriction on apart from being a real number,it is always possible to return a solution for (13). The blockingprobability for class- traffic is given by , suchbound should be tolerated by the traffic. Note that PDAC offersabsolute guarantees on bandwidth but not on blocking where thegoal is to satisfy (1). Again applying the asymptotic approxima-tion to in (13) we end up with the following low cost linearprogramming problem ( variables and constraints),(14)where: , and . The classpartitions returned from the solution of (14) provide an ap-proximated implementation for the PDAC service.III. LOAD ESTIMATIONIn order to return the link partitions from the relaxed problemin (14) it is necessary to determine all class loads in advance.However, in a real scenario class loads are likely to change dueto the dynamics involving session arrivals and departures. Wepropose a maximum likelihood estimator (MLE) for each thatcontinuously estimate loads from network observed states(number of class sessions in the system at time ). The Erlangformulae is used as the likelihood function,(15)Taking past independent samples, we have(16)The MLE is computed from(17)The fraction in the right term is simply the acceptance proba-bility, thus the MLE is reduced to(18)The samples are collected during each interval , anddirectly computed through the ratio between rejected and totalnumber of connection arrivals. A new PDAC problem is solvedat each and new class partitions obtained. Using a receiver-322 IEEE COMMUNICATIONS LETTERS, VOL. 8, NO. 5, MAY 2004Fig. 1. PDAC errors for Exp1, system scaled from  = 1 to  = 10 .oriented signalling protocol (e.g., RSVP) the response for a re-quest is acknowledged by the receiver and follows the backwardpath until it reaches the origin node. In this way, the loads can becomputed from (18) by all links along the path, and the PDACcan be independently implemented on each link using only lo-cally available information.IV. NUMERICAL RESULTSThe error incurred in any PDAC implementation can be calcu-lated taking the class of unitary weight, say class-1, as referenceand as the blocking ratio.(19)Equation (19) quantifies the deviations a given implementationmay produce from the goals set for PDAC (1), whereimplies in a precise implementation.We carried out two experiments to evaluate the performanceof a PDAC implementation based on asymptotic approximation.We used the same number of classes as observed in other PDS[1], in the first experiment (Exp1) we considered three classesof traffic while in the second (Exp2) we used four classes asshown in the table below:kb/s Mb/sThe parameter represents the scaling factor (multiplier),which is used to evaluate PDAC behavior under large scalesystems. Note that the limiting regime is reached when .Each gives a different problem whose solution (the partitions) is obtained from (14). After obtaining the partitions wecomputed the blocking probabilities and assessed the adequacyof the solutions in terms of the errors produced (19). Fig. 1shows PDAC errors for Exp1 where each curve representsthe results obtained for a different weight setting. It can beobserved that errors decrease as system scales, when thecapacity is close to 2 Gbps all errors fall below 1%. A similarbehavior was also observed in Fig. 2 for Exp2, however thesystem had to be scaled further to have all errors below 1%.Both figures showed accurate implementations of PDAC withclass partitions obtained from (14) as the scaling factor grows.Note that the main purpose of the scaling parameter was toshow how precision is improved when load, i.e., number offlows (up to 32 768 in Exp1 and below 327 680 in Exp2) andcapacity (BW) are scaled together.Fig. 2. PDAC errors for Exp2, system scaled from  = 1 to  = 10 .Fig. 3. Evaluation of the MLE in two different scenarios: loads changingabruptaly and with a cosine function.We also evaluate the performance of the load estimator pre-sented in Section III. Fig. 3 shows the results obtained for twodifferent scenarios: loads changing abruptly and loads changingaccording to a cosine function. A new estimation is returned ateach interval , which was chosen to be five times the meansession holding time (exponentially distributed). A maximumerror of 10.4% and mean error of 1.79% were observed. Othersettings were also tested, including deterministic holding times,showing high accuracy and robustness in relation to the inde-pendent sample assumption.V. CONCLUSIONWe proposed a service, the PDAC, which controls the admit-tance of traffic from different classes according to a predefinedset of weights. Such service conforms with the general idea be-hind the proportional differentiated model. PDAC is a scalableservice since it uses a class-based approach where the neces-sary per-flow management procedures in a practical implemen-tation are light. Given that PDAC involves the use of complexblocking probability equations we applied asymptotic approxi-mation to simplify the framework. Also we relaxed PDAC defi-nition to overcome feasibility problems imposed by the equalityconstraints in general PDS goal. We proposed an offered loadestimator and briefly discussed a practical implementation ofPDAC in the network. Finally, numerical results showed that ourapproximated solution was adequate, specially for large scaleproblems when the limiting regime approximation is precise.REFERENCES[1] C. Dovrolis, D. Stiliadis, and P. Ramanathan, “Proportional differenti-ated services: Delay differentiation and packet scheduling,” IEEE/ACMTrans. Networking, vol. 10, pp. 12–26, Feb. 2002.[2] K. W. Ross, Multiservice Loss Models for Broadband Telecommunica-tion Networks. New York: Springer-Verlag, 1995.[3] D. Jagerman, “Some properties of the Erlang loss function,” Bell Syst.Tech. J., vol. 53, no. 3, pp. 525–551, 1974.

Proportional differentiated admission control

R.M. Salles

J.A. Barria

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