Exact and Efficient Analysis of s-Staggered Setup Queues for Energy-Aware Data Centers

Dynamic ON–OFF server control is widely used to reduce energy consumption in data centers. We study ON–OFF control in a queueing system with an s-staggered setup policy, which limits the number of servers that can simultaneously enter the setup state. Despite its potential energy benefits, analytical results for this policy remain limited, particularly for large-scale systems with infinite buffers. This paper presents a generating-function-based analysis of the s-staggered setup queueing model and derives exact expressions for the stationary queue-length distribution. We enhance the conventional generating-function approach by reformulating the non-homogeneous part of the underlying Markov chain, thereby reducing the number of computational states and improving scalability. The proposed algorithm requires approximately half the computational effort of the conventional generating-function approach when s is small relative to system capacity. Numerical experiments demonstrate that the algorithm can efficiently handle large-scale systems and provides insights into the energy–performance trade-off.