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Feyaerts et al. mean arrival rate must be equal to the mean departure rate. Since departures only occur in phase 2 and that at a rate of 1 departure per slot, the mean departure rate is equal to p2 . So we find p2 = λ . (24) From (22) and (24) and the normalization condition, we get p1 = 1 − p0 − p2 . 6 (25) Customer Delay Distribution The customer delay is the integer number of slots a customer resides in the system, starting at the end of the customer’s arrival slot, until the end of the slot during which the customer leaves the system.

A Bernoulli arrival process and deterministic service times are assumed. We derive the steady-state probabilities of the system’s state as well as the distributions of the phase sojourn times and the customer delay. For the latter, we condition on the phase during the customer’s arrival slot. The influence of the model parameters on the results is discussed by means of a numerical example. 1 Introduction In a typical work-conserving queue under low to moderate load conditions, the service unit has to switch often between being idle and being busy.

K) , η (1) , . . , η (n−k) ) = lim P {it = i, nt = N, kt = k, t→∞ rt = 0, νt = ν, ζt = (l) ζ, ξt = ξ (l) , l = (m) 1, k, ηt = η (m) , m = 1, n − k}, i > 0; π(0, n, k, ν, 1, ζ, ψ, ξ (1) , . . , ξ (k) , η (1) , . . , η (n−k) ) = lim P {it = 0, nt = n, kt = k, t→∞ (l) (m) rt = 1, νt = ν, ζt = ζ, ψt = ψ, ξt = ξ (l) , l = 1, k, ηt = η (m) , m = 1, n − k}; π(i, k, 1, ν, ζ, ξ (1) , . . , ξ (k) , η (1) , . . , η (n−k) ) = lim P {it = i, nt = N, kt = k, t→∞ rt = 1, νt = ν, ζt = ζ, ψt = (l) ψ, ξt (l) (m) = ξ , l = 1, k, ηt = η (m) , m = 1, n − k}, i > 0.

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