TY - JOUR

T1 - On stabilizability of fluid multi-server polling systems with setups

AU - Матвеев, Алексей Серафимович

N1 - Funding Information: This research was supported by the Russian Science Foundation under the grant 14-21-00041p and was performed in Saint Petersburg State University.

PY - 2018

Y1 - 2018

N2 - A time-invariant fluid model of a polling system is considered. It consists of finitely many servers and buffers with unlimited sizes. The buffers receive inflows of work from the outside, work leaves the system after processing by a server. Every server works only with buffers from an associated zone of service, which may overlap for various servers, is able to serve at most one buffer at a time and so has to switch, from time to time, among buffers, the switch-over times are nonzero. We present a criterion for existence of a scheduling and service protocol that makes the system stable in the sense that the total amount of work in the buffers remains bounded as time progresses. The necessity part of this result is concerned with the widest class of protocols, including dynamic ones that are centralized and have access to the full information about the events in the system. Meanwhile, we show that every stabilizable system can be stabilized in a fully decentralized fashion via a simple static protocol, e.g., by a protocol that is based on independent round robin scheduling of the servers and for every server, employs only time measurement.

AB - A time-invariant fluid model of a polling system is considered. It consists of finitely many servers and buffers with unlimited sizes. The buffers receive inflows of work from the outside, work leaves the system after processing by a server. Every server works only with buffers from an associated zone of service, which may overlap for various servers, is able to serve at most one buffer at a time and so has to switch, from time to time, among buffers, the switch-over times are nonzero. We present a criterion for existence of a scheduling and service protocol that makes the system stable in the sense that the total amount of work in the buffers remains bounded as time progresses. The necessity part of this result is concerned with the widest class of protocols, including dynamic ones that are centralized and have access to the full information about the events in the system. Meanwhile, we show that every stabilizable system can be stabilized in a fully decentralized fashion via a simple static protocol, e.g., by a protocol that is based on independent round robin scheduling of the servers and for every server, employs only time measurement.

KW - Planning and scheduling

KW - Queues

KW - Service

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85049665088&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 26

EP - 34

JO - Cybernetics and Physics

JF - Cybernetics and Physics

SN - 2223-7038

IS - 1

ER -