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I. Agile ModelAgile is an iterative, team-based approach to development which emphasizes the rapid delivery of an application in complete functional components. Rather than creating tasks and schedules, all time is "timeboxed" into phases called "sprints." Each sprint has a defined duration (usually in weeks) with a running list of deliverables, planned one sprint in advance. Deliverables are prioritized by business value as determined by the customer. If all planned work for the sprint cannot be completed, work is reprioritized and the information is used for future sprint planning. As work is completed during each sprint, it is continuously reviewed and evaluated by the customer, who may be considered the most critical member of the AGILE team. As a result, Agile relies on a very high level of customer involvement throughout the project [5].There are various methodologies that are collectively known as agile, as they promote the values of the agile manifesto and they are consistent with the above principles. The most popular ones are: DSDM (Dynamic System Development Method)-is probably the original agile development method. DSDM was around before the term "agile" was even invented, but is absolutely based on all the principles we"ve come to know as agile. DSDM seems to be much less well-known outside of the UK [4] [7].Scrum-is also an agile development method, which concentrates particularly on how to manage tasks within a team-based development environment. Scrum is the most popular and widely adopted agile method -I think because it is relatively simple to implement and addresses many of the management issues that have plagued IT development teams for decades [3].XP-(Extreme Programming) is a more radical agile methodology, focusing more on the software engineering process and addressing the analysis, development and test phases with novel approaches that make a substantial difference to the quality of the end product [8].

Formal methods are the mathematically techniques and tools which are used at early stages of software development lifecycle processes. The utter need of using formal methods in safety critical system leads to accuracy, consistency and correctness in proposed system. In safety critical real time application, requirements should be unambiguous and very accurate which can be achieved by using mathematical theorems. There is utter need to focus on the requirement phase which is the most critical phase of SDLC. This paper focuses on the use of Z notation for incorporating the accuracy, consistency, and eliminates ambiguity in safety critical system: Road Traffic Management System as a case study. The syntax, semantics, type checking and domain checking are further verified by using Z/EVES: a Z notation type checker tool.

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