2018/05/23 by Khanik Kerobyan, R. Covington, Kerobyan, K. +5
Business, Management and Accounting · Computer Science · Decision Sciences · #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #FOS: Mathematics #Network Traffic and Congestion Control #Performance (cs.PF) #Probability (math.PR) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1805.09642
openalex publication_date 2018/05/23 · openalex created_date 2018/06/01 · openalex updated_date 2026/07/28
In the present paper the infinite-server MMAPkGk queueing model with random resource vector of customers, marked MAP arrival and semi-Markov (SM) arrival of catastrophes is considered. The joint generating functions (PGF) of transient and stationary distributions of number of busy servers and numbers of different types served customers, as well as Laplace transformations (LT) of joint distributions of total accumulated resources in the model at moment and total accumulated resources of served customers during time interval are found. The basic differential and renewal equations for transient and stationary PGF of queue sizes of customers are found.