Availability analysis of load-sharing systems

Markov reward models lend themselves naturally to a unified reliability and performance analysis of load-sharing systems. However, reliability and performance analyses are often done independently without realizing that the performance analyst's results should be used to assign rewards in the reliability analyst's Markov chains. As a result, a state's reward is approximated by N/sub i//N, where N/sub i/ is the number of surviving units in state i and N is the total number of units in a load-sharing system. This simplistic approach typically produces pessimistic availability estimates. This paper proposes a more vigorous reward assignment process that compares rewards from different perspectives using a modem pool in a remote access application as an example. First the equipment supplier's perspective is presented using GR-512. This approach produces an availability estimate that is typically used in bids. It is shown that if the equipment supplier follows GR-512, the product availability is presented in the best possible light. In contrast, following the above-mentioned simplistic approach would present the product availability in the worst possible light. The end-user's perspective gives a service availability (or accessibility) estimate, which is much lower than the equipment supplier's estimate. Whereas the equipment supplier considers the system to be perfect when it meets the engineered specification in its normal state, the end user would rate the normal state as less than perfect because some calls are blocked even when all units are working. As a result, the reward assigned by the end user to the normal state is less than 1; hence the service availability is lower than equipment availability. The end user's estimate is typically included in service-level agreements. Finally, we consider the service provider's revenue generating perspective. The service provider's availability estimate is found to be slightly lower than the equipment supplier's estimate. The difference is attributed to reward assignment during the low-traffic hours. The equipment supplier gives the system full credit (reward=1) when the capacity is greater than the demand even when the demand is zero. In contrast, the service provider only counts the served traffic (reward=0 if the demand is zero despite of a system operating at full capacity). In summary, we present load-sharing system availability from different perspectives and advocate combining performance and reliability analyses within the Markov reward framework.