Incremental Availability Evaluation Model for p-Cycle Protected Connections János Szigeti, Tibor Cinkler High-Speed Networks Laboratory Department of Telecommunications and Media Informatics Budapest University of Technology and Economics Magyar tudósok krt 2, H-1117 Budapest, Hungary Email: {szigeti,cinkler}@tmit.bme.hu Abstract— QoS routes need availability assurance. Regardless of the applied protection scheme, there are several heuristic algorithms that can approximate the availability of connections based on the availability parameters of network components along the connection path. Accurate approximation can be achieved with simple and fast calculation only for the most basic protection schemes, the more complex the protection scheme is the more complex and long running calculation is required to get the result. Though, the inaccuracy of the heuristic algorithms is negligible in the most cases of practical usage. In this paper we present an availability calculation method for p-cycles that exploits the special properties of the p-cycle protec- tion scheme and provides accurate results without enumerating all the possible network or protection configuration states. The method evaluates the availability of the connection along the working path link-by-link incrementally, pre-calculating also those conditional availabilities of the connection-part that may be used in latter calculations. Theoretically, the complexity of the algorithm is still O(2 n ), however, in fact n does not get high, moreover, it can be kept moderate low if the size of the cycles is constrained. Keywords: availability, conditional probability, p-cycle I. I NTRODUCTION Connection availability is a key issue in QoS routing. There are several protection schemes known which provide different grade of availability on the price of additional net- work resource usage. Whilst the network resource usage of the protection schemes may be measured easily, telling the accurate connection availability is usually a hard task. A. Protection schemes The classification of the protection schemes, partially pre- sented in [1], can be made along multiple dimensions, depend- ing on the manner of backup path planning: pre-calculation or restoration, the sharability of the backup resources, the range of the scheme: end-to-end path protection, path segment protection [2][3] or local, span protection (e.g. p-cycles [4] or RPR [5]). The different protection schemes can be compared to each other by means of protection activation/switching delay, con- trolling complexity, resource requirement and provided avail- ability. Whilst the most works in the field of optimization This work has been supported by the EC within the IST FP6 NoE e- Photon/ONe+ (http://www.e-photon-one.org) research framework. and algorithm development have focused on achieving near- optimal (i.e., minimal) resource usage, the availability, or more precisely said the availability evaluation, has been a marginal issue of the optimization methods. B. Availability To assure the availability of a connection many different methods can be used. The easiest way is to prove single fail- ure survivability. The formerly mentioned protection schemes protect against single failures. However, as the networks grow and the applications demand higher availability, assuring single failure survivability is not enough to decide the fulfillment of connection availability requirements. More complex methods are needed which count with multi- ple simultaneous failures. Dedicated 1+1 end-to-end protection can be evaluated as parallel switched series of devices [6], however, even in SBPP (shared backup path protection) other methods must be used because of the resource sharing (over- lapping, interfering). [7] traces back connection availability on link availabilities in networks without resource sharing, [8] suggests a method for estimating SBPP availability, [9] esti- mates connection availability by evaluating each combination of N failures in the network and giving an upper-bound for the estimation deviation, [10] investigates dual failures and [11] analyses multiple failures in p-cycles. Another possibility is using heuristics like Monte-Carlo simulation or Tabu-Search for estimating connection availability. The availabilities or, conversely, the failures can be modeled in several ways. The simplest solution is assigning a probabil- ity constant to each network equipment. This value, however, tells not much about the average length of the failures, which becomes important when we also deal with failure detection and other signaling times or when we take a look at the SLA contract made between the service provider and its client. For that reason, QoR [12] systems prefer availability given by Mean Time To Failure (MTTF) – Mean Time To Repair (MTTR) pairs, or MTTF replaced by Mean Time Between Failures (MTBF=MTTF-MTTR). Dealing with the MTTF/MTTR pair, i.e., deriving these values for parallel or serial connected devices, is not as easy as was with a single