ACM Transactions on Mathematical Software (TOMS)
On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications
Signals & systems (2nd ed.)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Waiting time, busy periods and output models of a server analyzed via Wiener-Hopf factorization
Performance Evaluation - Special issue on performance and control of network systems
Computing waiting-time probabilities in the discrete-time queue: GIX/G/1
Performance Evaluation
Exact aggregate solutions for M/G/1-type Markov processes
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Discrete-Time Models for Communication Systems Including ATM
Discrete-Time Models for Communication Systems Including ATM
Inverse Free Parallel Spectral Divide and Conquer Algorithms for
Inverse Free Parallel Spectral Divide and Conquer Algorithms for
Combined Elapsed Time and Matrix-Analytic Method for the Discrete Time GI/G/1 and GIX/G/1 Systems
Queueing Systems: Theory and Applications
System-theoretical algorithmic solution to waiting times in semi-Markov queues
Performance Evaluation
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In this paper, we study the discrete time Lindley equation governing an infinite size GI/GI/1 queue. In this queuing system, the arrivals and services are independent and identically distributed but they obey a discrete time matrix geometric distribution not necessarily with finite support. Our GI/GI/1 model allows geometric batch arrivals and also treats late, early, and hybrid arrival models in a unified manner. We reduce the problem of finding the steady state probabilities for the Lindley equation to finding the generalized ordered Schur form of a matrix pair (E, A) where the size of these matrices are the sum, not the product, of the orders of individual arrival and service distributions. The approach taken in this paper is purely matrix analytical and we obtain a matrix geometric representation for the related quantities (queue lengths or waiting times) for the discrete time GI/GI/1 queue using this approach.