Transient Analysis of a State-dependent Queueing Network With Finite Capacity

2002 ◽  
Vol 79 (4) ◽  
pp. 391-401
Author(s):  
P.R. Parthasarathy ◽  
Wolfgang Stadje ◽  
R.B. Lenin
Keyword(s):  
Transient Analysis ◽  
Queueing Network ◽  
Finite Capacity ◽  
State Dependent

Transient analysis of state-dependent queueing networks via cumulant functions

2001 ◽  
Vol 38 (04) ◽  
pp. 841-859 ◽  
Author(s):  
Timothy I. Matis ◽  
Richard M. Feldman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Queueing Networks ◽  
Transient Analysis ◽  
Queueing Network ◽  
Partial Differential ◽  
Cumulant Generating Function ◽  
State Dependent ◽  
Intensity Functions ◽  
First Moment

A new procedure that generates the transient solution of the first moment of the state of a Markovian queueing network with state-dependent arrivals, services, and routeing is developed. The procedure involves defining a partial differential equation that relates an approximate multivariate cumulant generating function to the intensity functions of the network. The partial differential equation then yields a set of ordinary differential equations which are numerically solved to obtain the first moment.

Transient analysis of state-dependent queueing networks via cumulant functions

2001 ◽  
Vol 38 (4) ◽  
pp. 841-859 ◽  
Author(s):  
Timothy I. Matis ◽  
Richard M. Feldman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Queueing Networks ◽  
Transient Analysis ◽  
Queueing Network ◽  
Partial Differential ◽  
Cumulant Generating Function ◽  
State Dependent ◽  
Intensity Functions ◽  
First Moment

A new procedure that generates the transient solution of the first moment of the state of a Markovian queueing network with state-dependent arrivals, services, and routeing is developed. The procedure involves defining a partial differential equation that relates an approximate multivariate cumulant generating function to the intensity functions of the network. The partial differential equation then yields a set of ordinary differential equations which are numerically solved to obtain the first moment.

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 Heavy-Traffic Limits for a Many-Server Queueing Network with Switchover

2013 ◽  
Vol 45 (3) ◽  
pp. 645-672 ◽  
Author(s):  
Guodong Pang ◽  
David D. Yao
Keyword(s):  
Load Balancing ◽  
Differential Equations ◽  
Piecewise Linear ◽  
Heavy Traffic ◽  
Queueing Network ◽  
State Dependent ◽  
Diffusion Limits ◽  
Qed Regime ◽  
The Many ◽  
And Diffusion

We study a multiclass Markovian queueing network with switchover across a set of many-server stations. New arrivals to each station follow a nonstationary Poisson process. Each job waiting in queue may, after some exponentially distributed patience time, switch over to another station or leave the network following a probabilistic and state-dependent mechanism. We analyze the performance of such networks under the many-server heavy-traffic limiting regimes, including the critically loaded quality-and-efficiency-driven (QED) regime, and the overloaded efficiency-driven (ED) regime. We also study the limits corresponding to mixing the underloaded quality-driven (QD) regime with the QED and ED regimes. We establish fluid and diffusion limits of the queue-length processes in all regimes. The fluid limits are characterized by ordinary differential equations. The diffusion limits are characterized by stochastic differential equations, with a piecewise-linear drift term and a constant (QED) or time-varying (ED) covariance matrix. We investigate the load balancing effect of switchover in the mixed regimes, demonstrating the migration of workload from overloaded stations to underloaded stations and quantifying the load balancing impact of switchover probabilities.

Braess's paradox in a queueing network with state-dependent routing

1997 ◽  
Vol 34 (01) ◽  
pp. 134-154 ◽  
Author(s):  
Bruce Calvert ◽  
Wiremu Solomon ◽  
Ilze Ziedins
Keyword(s):  
Queueing Network ◽  
Wheatstone Bridge ◽  
The Other ◽  
Time Of Arrival ◽  
Expected Time ◽  
Initial Network ◽  
Braess’S Paradox ◽  
State Dependent ◽  
Service Rates ◽  
Queue Lengths

We consider initially two parallel routes, each of two queues in tandem, with arriving customers choosing the route giving them the shortest expected time in the system, given the queue lengths at the customer's time of arrival. All interarrival and service times are exponential. We then augment this network to obtain a Wheatstone bridge, in which customers may cross from one route to the other between queues, again choosing the route giving the shortest expected time in the system, given the queue lengths ahead of them. We find that Braess's paradox can occur: namely in equilibrium the expected transit time in the augmented network, for some service rates, can be greater than in the initial network.

scholarly journals A Paradox in a Queueing Network with State-Dependent Routing and Loss

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Ilze Ziedins
Keyword(s):  
Optimal Policy ◽  
Queueing Network ◽  
Service Rate ◽  
Tandem Queues ◽  
Finite Systems ◽  
Second Stage ◽  
State Dependent ◽  
Optimal Policies ◽  
System Optimal ◽  
Two Stages

Consider a network of parallel finite tandem queues with two stages, where each arrival attempts to minimize its own cost due to loss. It is known that the user optimal and asymptotic system optimal policies may differ—we give examples showing that they may differ for finite systems and that as the service rate is increased at the second stage the user optimal policy may change in such a way that the total expected cost due to loss increases.

Sign in / Sign up

Export Citation Format

Share Document