Analysis of MAP(1), MAP(2)/ PH/ 1 non-preemptive priority queueing model under classical retrial policy with breakdown, repair, discouragement, single vacation, standby server, negative arrival and impatient customers

DOI10.1007/s40819-021-01126-yzbMath1499.60315OpenAlexW3193385984WikidataQ114852181 ScholiaQ114852181MaRDI QIDQ2114634

Yanyan Li

Publication date: 15 March 2022

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40819-021-01126-y

zbMATH Keywords

MAPsingle vacationdiscouragementimpatient behaviourPH distributionsstandby server

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20)

Cites Work

• Matrix-analytic methods in queueing theory
• A single-server discrete-time retrial \(G\)-queue with server breakdowns and repairs
• A retrial queue with redundancy and unreliable server
• Analysis of a retrial queuing model with MAP arrivals and two types of customers.
• Quasi-birth-and-death Markov processes with a tree structure and the MMAP[K/PH[K]/N/LCFS non-preemptive queue]
• \(G\)-networks: A versatile approach for work removal in queueing networks
• \(MAP_ 1,MAP_ 2/M/c\) retrial queue with the retrial group of finite capacity and geometric loss.
• An \(\mathrm{M}^{[X}/\mathrm{G}(a,b)/1\) queueing system with breakdown and repair, stand-by server, multiple vacation and control policy on request for re-service]
• Transient analysis of \(\mathrm{M}^{[X_1},\mathrm{M}^{[X_2]}/\mathrm{G}_1,\mathrm{G}_2/1\) retrial queueing system with priority services, working vacations and vacation interruption, emergency vacation, negative arrival and delayed repair]
• On the steady-state system size distribution for a discrete-time \(\mathrm{Geo}/\mathrm{G}/1\) repairable queue
• The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service
• A disaster queue with Markovian arrivals and impatient customers
• The BMAP/PH/N retrial queue with Markovian flow of breakdowns
• A RETRIAL QUEUEING MODEL WITH MAP ARRIVALS, CATASTROPHIC FAILURES WITH REPAIRS, AND CUSTOMER IMPATIENCE
• A single-server queue with server vacations and a class of non-renewal arrival processes
• A versatile Markovian point process
• Product-form queueing networks with negative and positive customers
• A logarithmic reduction algorithm for quasi-birth-death processes
• Steady state solution of a single-server queue with linear repeated requests
• On a single server queue with negative arrivals and request repeated