Customer-Decay Approximations for the M/G/C Queue with Heterogenous Servers Sulaiman S. 1* 1 Department of Mathematics, Umaru Musa Yar’Adua University Katsina-Nigeria. Daman O.A, Olabode B.T and Basimanebotlhe O.S Department of Mathematics, University of Botswana, Gaborone, Botswana. September 11, 2012 Abstract This paper provides numerical approximations to partial differential equa- tion describing customer decay in a heterogenous server M/G/C queue with (C-1) exponential servers and a single regularly varying general server of Poi- son arrival process. The decay approximations were obtained given that, the service distribution of the general server is regularly varying at infinity index -ψ. We generalized the decay equation for the M/G/2 to the M/G/C (C ≥ 2), develop a MATLAB algorithm for simulation and finally, generate numerical approximations for certain values of C and μ, the service rate of a single ex- ponential server. In addition to the partial differential equation derived, the numerical approximation obtained shows that, the generating function G(p,η) for the expected number of customers in the system depends on the size of the service rate and that an extreme minimum exist for an arbitrary G(p,η) in a closed bounded set [a,b] for a,b ∈ R. Also, it is shown that G(p,η) depends on the number of exponential servers in the system which strictly determines the turning point for the generating function G(p,η). In conclusion, the result obtained in this work applies to only customer systems with high waiting inten- sity p since; there exist strong convergence of δt → 0, a.s. between successive arrivals and departures from such systems. Keywords: M/G/C Queue, Customer-Decay Process, Generating Function and Regularly Varying Function. Corresponding author: Sulaiman S. * ; man15j@yahoo.com 1