The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity

1983/12/01 by W. Grassmann, Winfried K. Grassmann · 1 citation
Business, Management and Accounting · Engineering · Mathematics · #Advanced Queuing Theory Analysis #Burke's theorem #Combinatorics #Computer network #Computer science #Convexity #Discrete mathematics #Fork–join queue #Geometry #Intensity (physics) #Mathematics #Optimization and Packing Problems #Physics #Queue #Queue management system #Queueing theory #Regular polygon #Statistics #Traffic intensity #graph theory and CDMA systems

paper · doi:10.2307/3213605

openalex publication_date 1983/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

In this paper, we show that the expected number in an M / M / c queue is convex with respect to the traffic intensity. The proof is conducted by expressing the second derivative of the expected queue size as the sum of non-negative terms.

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