On the estimation of moments of regenerative cycles in a general closed central-server queueing network

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

Download Full-text

A Queueing Network Analysis of a Hierarchical Communication Architecture for Advanced Metering Infrastructure

IEEE Transactions on Smart Grid ◽

10.1109/tsg.2021.3088879 ◽

2021 ◽

pp. 1-1

Author(s):

Jin Seek Choi ◽

Sungwhan Lee ◽

Se Joon Chun

Keyword(s):

Network Analysis ◽

Queueing Network ◽

Advanced Metering Infrastructure ◽

Communication Architecture ◽

Hierarchical Communication ◽

Advanced Metering

Download Full-text

Tail Asymptotics for Monotone-Separable Networks

Journal of Applied Probability ◽

10.1017/s002190020011784x ◽

2007 ◽

Vol 44 (02) ◽

pp. 306-320

Author(s):

Marc Lelarge

Keyword(s):

Queueing Network ◽

Network Models ◽

Moment Generating Function ◽

Stochastic Petri Nets ◽

Arrival Process ◽

Polling Systems ◽

Tail Asymptotics ◽

State Variables ◽

Monotone Functions ◽

Jackson Networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

Download Full-text