We consider single-server loss systems with exponential service times and non-stationary Poisson input. We prove that if the arrival rate is given by a periodic function, the proportion of lost customers is convex increasing in the amplitude.
Svoronos, Antony, and Linda Green. "A convexity result for single-server exponential loss systems with non-stationary arrivals." Journal of Applied Probability 25, no. 1 (March 1988): 224-227.
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