Defining Steady-State Service Level Agreeability using Semi-Markov Process

The ability of the servers to deliver services to the clients according to pre-defined agreements is becoming an important requirement. These pre-defined agreements are sometimes referred to as service level agreements (SLA). In most practical cases, these agreements are based on the response times observed by the customer. This service level ‘agreeability’ is not captured in the definitions of availability. A guarantee of server’s five-nines availability does not imply any guarantees to its service level agreements. System might be available most of the time, but it might not be satisfying the service level agreements. Although there is lot of work on making the systems satisfy service level agreements, the notion of service-level agreeability is not mathematically defined. Such definition should be useful in practice to compare service level agreements between different systems. In this paper, we attempt to mathematically characterize measurement-based steadystate service level agreeability. This definition is on the assumption that service-level agreements are based on response times. This assumption should be valid in practice, because ultimately all pre-defined agreements should result in the improved response-times observed by the customers of the system. Our characterization of service level agreeability is very much similar to the definition of steady-state availability [1]. System at any given point of time can be in one state of a set of possible states (S1, .. , SN ). In our definition, the set of possible states are divided based on threshold responsetime into two mutually exclusive sets SLA Satisfying States and SLA Violating States. We define the instantaneous service level agreeability SLA(t) of a system as the probability that the system is in one of the SLA satisfying states at time t. Often we are interested in the state of the system after a sufficiently long time has elapsed. For this purpose, we define the steady-state service level agreeability (or simply