Stability of multi-class queueing systems with state-dependent service rates

2006 ◽  
Author(s):  
Matthieu Jonckheere ◽  
Sem Borst
Keyword(s):  
Queueing Systems ◽  
State Dependent ◽  
Service Rates

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

Optimal Control of State-Dependent Service Rates in a MAP/M/1 Queue

2017 ◽  
Vol 62 (10) ◽  
pp. 4965-4979 ◽  
Author(s):  
Li Xia ◽  
Qi-Ming He ◽  
Attahiru Sule Alfa
Keyword(s):  
Optimal Control ◽  
State Dependent ◽  
Service Rates

scholarly journals On intensities of modulated Cox measures

1998 ◽  
Vol 11 (3) ◽  
pp. 411-423 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Stochastic Process ◽  
Stochastic Models ◽  
Queueing Systems ◽  
Random Measure ◽  
Random Measures ◽  
Explicit Formulas ◽  
State Dependent

In this paper we introduce and study functionals of the intensities of random measures modulated by a stochastic process ξ, which occur in applications to stochastic models and telecommunications. Modulation of a random measure by ξ is specified for marked Cox measures. Particular cases of modulation by ξ as semi-Markov and semiregenerative processes enabled us to obtain explicit formulas for the named intensities. Examples in queueing (systems with state dependent parameters, Little's and Campbell's formulas) demonstrate the use of the results.

scholarly journals SCHEDULING IN A SINGLE-SERVER QUEUE WITH STATE-DEPENDENT SERVICE RATES

2019 ◽  
Vol 34 (4) ◽  
pp. 507-521
Author(s):  
Urtzi Ayesta ◽  
Balakrishna Prabhu ◽  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Arrival Rate ◽  
Complete Characterization ◽  
Single Server ◽  
Holding Costs ◽  
Release Times ◽  
State Dependent ◽  
Service Rates ◽  
Transient System ◽  
The Cost

We consider single-server scheduling to minimize holding costs where the capacity, or rate of service, depends on the number of jobs in the system, and job sizes become known upon arrival. In general, this is a hard problem, and counter-intuitive behavior can occur. For example, even with linear holding costs the optimal policy may be something other than SRPT or LRPT, it may idle, and it may depend on the arrival rate. We first establish an equivalence between our problem of deciding which jobs to serve when completed jobs immediately leave, and a problem in which we have the option to hold on to completed jobs and can choose when to release them, and in which we always serve jobs according to SRPT. We thus reduce the problem to determining the release times of completed jobs. For the clearing, or transient system, where all jobs are present at time 0, we give a complete characterization of the optimal policy and show that it is fully determined by the cost-to-capacity ratio. With arrivals, the problem is much more complicated, and we can obtain only partial results.

Throughput properties of a queueing network with distributed dynamic routing and flow control

1996 ◽  
Vol 28 (01) ◽  
pp. 285-307 ◽  
Author(s):  
Leandros Tassiulas ◽  
Anthony Ephremides
Keyword(s):  
Flow Control ◽  
Rate Control ◽  
Queueing Network ◽  
Local State ◽  
Service Rate ◽  
Maximum Throughput ◽  
State Information ◽  
Arbitrary Topology ◽  
State Dependent ◽  
Service Rates

A queueing network with arbitrary topology, state dependent routing and flow control is considered. Customers may enter the network at any queue and they are routed through it until they reach certain queues from which they may leave the system. The routing is based on local state information. The service rate of a server is controlled based on local state information as well. A distributed policy for routing and service rate control is identified that achieves maximum throughput. The policy can be implemented without knowledge of the arrival and service rates. The importance of flow control is demonstrated by showing that, in certain networks, if the servers cannot be forced to idle, then no maximum throughput policy exists when the arrival rates are not known. Also a model for exchange of state information among neighboring nodes is presented and the network is studied when the routing is based on delayed state information. A distributed policy is shown to achieve maximum throughput in the case of delayed state information. Finally, some implications for deterministic flow networks are discussed.

scholarly journals Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

2018 ◽  
Vol 28 (1) ◽  
pp. 141-154 ◽  
Author(s):  
Alexander Zeifman ◽  
Rostislav Razumchik ◽  
Yacov Satin ◽  
Ksenia Kiseleva ◽  
Anna Korotysheva ◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Queueing Systems ◽  
Approximation Error ◽  
Linear Operators ◽  
Upper And Lower Bounds ◽  
Logarithmic Norm ◽  
Batch Arrivals ◽  
State Dependent ◽  
The Mean ◽  
Number Of Customers

AbstractIn this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.

Some distributional approximations in Markovian queueing networks

1982 ◽  
Vol 14 (03) ◽  
pp. 654-671 ◽  
Author(s):  
T. C. Brown ◽  
P. K. Pollett
Keyword(s):  
Queueing Networks ◽  
Poisson Processes ◽  
Single Class ◽  
Open Network ◽  
State Dependent ◽  
Service Rates ◽  
Distributional Approximations ◽  
Closed Network ◽  
Poisson Approximations ◽  
Markovian Queueing Networks

We consider single-class Markovian queueing networks with state-dependent service rates (the immigration processes of Whittle (1968)). The distance of customer flows from Poisson processes is estimated in both the open and closed cases. The bounds on distances lead to simple criteria for good Poisson approximations. Using the bounds, we give an asymptotic, closed network version of the ‘loop criterion' of Melamed (1979) for an open network. Approximation of two or more flows by independent Poisson processes is also studied.

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