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In project management, efficiency of team performance is often associated with the balance in terms of its team roles. All explanations, however, as well as conclusions that relate to balancing a project team, were obtained verbally and are not confirmed either theoretically or empirically. Therefore, it is appropriate to examine the transitions between team roles based on mathematical modeling. To understand regularities in the transitions of team members between team roles, we constructed a transition model based on the discrete Markov chain and defined parameters of the model. Using the simulation, we performed the study and demonstrated that it is natural for a software development project team to balance the team roles. This attribute does not depend on the initial composition of the team in terms of team roles. A difference in initial conditions only affects the rate of change in the probabilities of individual team roles, but the attribute of reducing the difference between the values of probabilities of individual team roles persists. The results obtained confirm that by helping some team members to take on secondary roles to prevent the duplication of roles or to resolve certain problems, a project manager may influence the balancing of team in terms of team roles.

Examining the attributes of transitions between team roles in the software development projects