Software maintenance is an important activity in software engineering. Over the decades, software maintenance costs have been continually reported to account for a large majority of software costs [Zelkowitz 1979, Boehm 1981, McKee 1984, Boehm 1988, Erlikh 2000]. This fact is not surprising. On the one hand, software environments and requirements are constantly changing, which lead to new software system upgrades to keep pace with the changes. On the other hand, the economic benefits of software reuse have encouraged the software industry to reuse and enhance the existing systems rather than to build new ones [Boehm 1981, 1999]. Thus, it is crucial for project managers to estimate and manage the software maintenance costs effectively. / Accurate cost estimation of software projects is one of the most desired capabilities in software development Process. Accurate cost estimates not only help the customer make successful investments but also assist the software project manager in coming up with appropriate plans for the project and making reasonable decisions during the project execution. Although there have been reports that software maintenance accounts for the majority of the software total cost, the software estimation research has focused considerably on new development and much less on maintenance. Now if we talk about real time software system(RTSS) development cost estimation and maintenance cost estimation is not much differ from simple software but some critical factor are considered for RTSS development and maintenance like response time of software for input and processing time to give correct output. As like simple software maintenance cost estimation existing models (i.e. Modified COCOMO-II) can be used but after inclusion of some critical parameters related to RTSS. A Hypothetical Expert input and an industry data set of eighty completed software maintenance projects were used to build the model for RTSS maintenance cost. The full model, which was derived through the Bayesian analysis, yields effort estimates within 30% of the actual 51% of the time,outperforming the original COCOMO II model when it was used to estimate theseprojects by 34%. Further performance improvement was obtained when calibrating the full model to each individual program, generating effort estimates within 30% of the actual 80% of the time.