en Applied Probability and Queuing Theory Applied Probability and Queuing Theory پژوهشی Original Here, a two server queueing system with Poisson arrivals and two different types of customers (M/H2/2 queue) is analyzed. A novel straightforward method is presented to acquire the exact and explicit forms of the performance measures. First, the steady state equations along with their Z-transforms are derived for the aforementioned queueing system. Using some limiting behaviors of the steady-state probabilities along with partial fraction decomposition as a simple algebraic procedure, the problem reduces to the solution of a system of linear equations. Queueing systems, Hyper-exponential service times, Z-transform, Partial fraction decomposition 55 63 http://iors.ir/journal/browse.php?a_code=A-10-519-1&slc_lang=en&sid=1 J. Arkat j.arkat@uok.ac.ir 00031947532846001292 00031947532846001292 Yes Department of Industrial Engineering University of Kurdistan, Sanandaj, Iran M. Hosseinabadi Farahani m.hosseinabadi@ut.ac.ir 00031947532846001293 00031947532846001293 No Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran