TY - JOUR

T1 - Group service system with three queues and load balancing

AU - Savelov, Maxim P.

N1 - Funding statement: The study was supported by the Russian Fund of Basic Research (grant № 17-11-01173). Publisher Copyright: © 2022 Walter de Gruyter GmbH, Berlin/Boston.

PY - 2022/8/1

Y1 - 2022/8/1

N2 - A group service system for three queues is considered. At each time t = 1, 2,⋯, with some probability, a customer enters the system, selects randomly two queues, and goes to the shorter one. At each moment such that there is at least one customer in each queue, each queue performs instantly the service of one customer. By means of Lyapunov functions, a criterion for the ergodicity of the Markov chain corresponding to this queuing system is established. The limiting joint distribution of queue lengths is found, and the connection with the problem of balanced allocations of particles into cells is described. In the corresponding problem of balanced allocation of particles, the limiting distribution of the range is found, i. e. the difference between the maximal and minimal numbers of particles in cells.

AB - A group service system for three queues is considered. At each time t = 1, 2,⋯, with some probability, a customer enters the system, selects randomly two queues, and goes to the shorter one. At each moment such that there is at least one customer in each queue, each queue performs instantly the service of one customer. By means of Lyapunov functions, a criterion for the ergodicity of the Markov chain corresponding to this queuing system is established. The limiting joint distribution of queue lengths is found, and the connection with the problem of balanced allocations of particles into cells is described. In the corresponding problem of balanced allocation of particles, the limiting distribution of the range is found, i. e. the difference between the maximal and minimal numbers of particles in cells.

KW - balanced allocations of particles into cells

KW - choosing the shortest queue

KW - ergodicity

KW - Lyapunov function

KW - Markov chain

KW - queue systems with balanced load

KW - range

UR - http://www.scopus.com/inward/record.url?scp=85138461737&partnerID=8YFLogxK

U2 - 10.1515/dma-2022-0019

DO - 10.1515/dma-2022-0019

M3 - Article

AN - SCOPUS:85138461737

VL - 32

SP - 219

EP - 231

JO - Discrete Mathematics and Applications

JF - Discrete Mathematics and Applications

SN - 0924-9265

IS - 4

ER -