Lattice path counting and the theory of queues

DOI10.1016/j.jspi.2010.01.013zbMath1193.60106OpenAlexW2073075580MaRDI QIDQ972819

B. E. Eshmatov

Publication date: 21 May 2010

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2010.01.013

zbMATH Keywords

Markovian queueslattice pathstransient analysismultidimensional pathspaths in a quarter plane

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (5)

On lattice path counting and the random product representation, with applications to the \(E_r/M/1\) queue and the \(M/E_r/1\) queue ⋮ Waiting times in classical priority queues via elementary lattice path counting ⋮ From enumerating to generating: a linear time algorithm for generating 2D lattice paths with a given number of turns ⋮ A base-stock inventory model with service differentiation and response time guarantees ⋮ A combinatorial study of two-periodic random walks

Cites Work

• Walks in the quarter plane: Kreweras' algebraic model
• Coincidence probabilities
• A new method for solving a class of ballot problems
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• On the Karlin-McGregor theorem and applications
• On the enumeration and generation of generalized Dyck words
• Basic analytic combinatorics of directed lattice paths
• Dual processes to solve single server systems
• Two Parallel Queues Created by Arrivals with Two Demands I
• Random Walk in a Weyl Chamber
• Two parallel processors with coupled inputs
• The Time-Dependent Problem for a Queue with Preemptive Priorities
• Some Aspects of the Random Sequence
• Simple Random Walk and Rank Order Statistics
• Spectral theory for the differential equations of simple birth and death processes
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