“…Here only single traffic source in under consideration having constant bit rate C BW and a constant data packet size. If P S is the intensity of needs access and can be given by relation (9) In favor of the service rate of needs, the following equation is valid For k number of requirements to come in the FIFO system, the valid probability is given by: (11) In support of the mean time the requirement use up within the system, the valid mean time is given by (12) Here 1/μ = service time of one requirement. Subsequently, in support of the average number of requirements with in N number of system, the valid average mean time is given by: (13) As long as the switch has data from M number of origins and uses Poisson's distribution, λ = intensity of needs access [s -1 ] for all M sources is given by: (14) provided same codec for compressing the data from all M origins and make data packets of equal length and further transmit time for each and every packet at output is considered to be constant, the reference ( 14) can be simplified as follows: (15) By knowledge of transfer rate over the output line and packet processing time for the specific switch, it is feasible to identify the service rate of the specific system after association of ( 5) and ( 6) to the relation (10) and is given by: (16) Subsequent to association of ( 15) and ( 16) to the reference (8) we get relation for the overloading of system and are given by: (17) following association of ( 15), ( 16) and ( 17) to ( 12) we obtain the relation for mean service time and is given by: (18) Similarly subsequent to ( 15), ( 16) and ( 17) to (11) the valid relation for the probability of exactly k number requirements within the system; k≥2 (19) Thence, the service time using ( 16) for the service rate, the relation for delay probability is given by: (20) The equation ( 18) defines the average packet time delay within the switch, and equation ( 20), defines the probability distribution of the declared time delay, in addition to jointly they make the mathematical model of the time delay within the switch.…”