Optimal control of single-server queueing networks

1993 ◽  
Vol 37 (2) ◽  
pp. 187-205 ◽  
Author(s):  
Svend-Holger Friis ◽  
Ulrich Rieder ◽  
J�rgen Weishaupt
Keyword(s):  
Optimal Control ◽  
Queueing Networks ◽  
Single Server

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

On the optimal control of a single-server queueing system: Reply

1978 ◽  
Vol 26 (3) ◽  
pp. 463-464 ◽  
Author(s):  
C. H. Scott ◽  
T. R. Jefferson
Keyword(s):  
Optimal Control ◽  
Queueing System ◽  
Single Server

scholarly journals Optimal control of queueing networks: an approach via fluid models

2002 ◽  
Vol 34 (02) ◽  
pp. 313-328
Author(s):  
Nicole Bäuerle
Keyword(s):  
Optimal Control ◽  
Decision Rule ◽  
Average Cost ◽  
Queueing Networks ◽  
Optimal Decision ◽  
Stochastic Network ◽  
Asymptotically Optimal ◽  
Multiclass Queueing Networks ◽  
Optimal Decision Rule ◽  
Multiclass Queueing

We consider a general control problem for networks with linear dynamics which includes the special cases of scheduling in multiclass queueing networks and routeing problems. The fluid approximation of the network is used to derive new results about the optimal control for the stochastic network. The main emphasis lies on the average-cost criterion; however, the β-discounted as well as the finite-cost problems are also investigated. One of our main results states that the fluid problem provides a lower bound to the stochastic network problem. For scheduling problems in multiclass queueing networks we show the existence of an average-cost optimal decision rule, if the usual traffic conditions are satisfied. Moreover, we give under the same conditions a simple stabilizing scheduling policy. Another important issue that we address is the construction of simple asymptotically optimal decision rules. Asymptotic optimality is here seen with respect to fluid scaling. We show that every minimizer of the optimality equation is asymptotically optimal and, what is more important for practical purposes, we outline a general way to identify fluid optimal feedback rules as asymptotically optimal. Last, but not least, for routeing problems an asymptotically optimal decision rule is given explicitly, namely a so-called least-loaded-routeing rule.

Extremal properties of the FIFO discipline in queueing networks

1992 ◽  
Vol 29 (4) ◽  
pp. 967-978 ◽  
Author(s):  
Rhonda Righter ◽  
J. George Shanthikumar
Keyword(s):  
Likelihood Ratio ◽  
Service Time ◽  
Queueing Networks ◽  
Service Rate ◽  
Service Discipline ◽  
Single Server ◽  
Single Server Queues ◽  
First Results ◽  
Service Times ◽  
Number Of Customers

We show that using the FIFO service discipline at single server stations with ILR (increasing likelihood ratio) service time distributions in networks of monotone queues results in stochastically earlier departures throughout the network. The converse is true at stations with DLR (decreasing likelihood ratio) service time distributions. We use these results to establish the validity of the following comparisons:(i) The throughput of a closed network of FIFO single-server queues will be larger (smaller) when the service times are ILR (DLR) rather than exponential with the same means.(ii) The total stationary number of customers in an open network of FIFO single-server queues with Poisson external arrivals will be stochastically smaller (larger) when the service times are ILR (DLR) rather than exponential with the same means.We also give a surprising counterexample to show that although FIFO stochastically maximizes the number of departures by any time t from an isolated single-server queue with IHR (increasing hazard rate, which is weaker than ILR) service times, this is no longer true for networks of more than one queue. Thus the ILR assumption cannot be relaxed to IHR.Finally, we consider multiclass networks of exponential single-server queues, where the class of a customer at a particular station determines its service rate at that station, and show that serving the customer with the highest service rate (which is SEPT — shortest expected processing time first) results in stochastically earlier departures throughout the network, among all preemptive work-conserving policies. We also show that a cµ rule stochastically maximizes the number of non-defective service completions by any time t when there are random, agreeable, yields.

On the optimal control of a single-server queueing system: Comment

1978 ◽  
Vol 26 (3) ◽  
pp. 457-462 ◽  
Author(s):  
C. F. Klein ◽  
W. A. Gruver
Keyword(s):  
Optimal Control ◽  
Queueing System ◽  
Single Server

Characterizations of Poisson traffic streams in Jackson queueing networks

1979 ◽  
Vol 11 (02) ◽  
pp. 422-438 ◽  
Author(s):  
Benjamin Melamed
Keyword(s):  
Queueing Networks ◽  
Simple Graph ◽  
Single Server ◽  
Jackson Network ◽  
Jackson Networks ◽  
Equilibrium Behavior ◽  
Poisson Arrivals ◽  
Stochastic Properties ◽  
Networks Of Queues ◽  
Traffic Processes

The equilibrium behavior of Jackson queueing networks (Poisson arrivals, exponential servers and Bernoulli switches) has recently been investigated in some detail. In particular, it was found that in equilibrium, the traffic processes on the so-called exit arcs of a Jackson network with single server nodes constitute Poisson processes—a result extending Burke's theorem from single queues to networks of queues. A conjecture made by Burke and others contends that the traffic processes on non-exit arcs cannot be Poisson in equilibrium. This paper proves this conjecture to be true for a variety of Jackson networks with single server nodes. Subsequently, a number of characterizations of the equilibrium traffic streams on the arcs of open Jackson networks emerge, whereby Poisson-related stochastic properties of traffic streams are shown to be equivalent to a simple graph-theoretical property of the underlying arcs. These results then help to identify some inherent limitations on the feasibility of equilibrium decompositions of Jackson networks, and to point out conditions under which further decompositions are ‘approximately’ valid.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (2) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network.This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

scholarly journals Optimal control of some queueing networks

1992 ◽  
Vol 16 (5) ◽  
pp. 3-12
Author(s):  
Y. Yavin ◽  
C. Frangos
Keyword(s):  
Optimal Control ◽  
Queueing Networks

On stability of queueing networks with job deadlines

2003 ◽  
Vol 40 (2) ◽  
pp. 293-304 ◽  
Author(s):  
Amy R. Ward ◽  
Nicholas Bambos
Keyword(s):  
Sojourn Time ◽  
Queueing Networks ◽  
Single Server ◽  
Single Server Queue ◽  
Interesting Phenomenon ◽  
Single Node ◽  
Service Disciplines ◽  
Server Queue ◽  
Weakly Stable ◽  
Networks Of Queues

In this paper, we consider a single-server queue with stationary input, where each job joining the queue has an associated deadline. The deadline is a time constraint on job sojourn time and may be finite or infinite. If the job does not complete service before its deadline expires, it abandons the queue and the partial service it may have received up to that point is wasted. When the queue operates under a first-come-first served discipline, we establish conditions under which the actual workload process—that is, the work the server eventually processes—is unstable, weakly stable, and strongly stable. An interesting phenomenon observed is that in a nontrivial portion of the parameter space, the queue is weakly stable, but not strongly stable. We also indicate how our results apply to other nonidling service disciplines. We finally extend the results for a single node to acyclic (feed-forward) networks of queues with either per-queue or network-wide deadlines.

Calculation of sensitivities of throughputs and realization probabilities in closed queueing networks with finite buffer capacities

1989 ◽  
Vol 21 (1) ◽  
pp. 181-206 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Perturbation Analysis ◽  
Queueing Networks ◽  
Queueing Network ◽  
Theoretical Background ◽  
System Throughput ◽  
Single Server ◽  
Finite Buffer ◽  
Closed Queueing Networks ◽  
Steady State Probability ◽  
Single Class

Perturbation analysis is an efficient approach to estimating the sensitivities of the performance measures of a queueing network. A new notion, called the realization probability, provides an alternative way of calculating the sensitivity of the system throughput with respect to mean service times in closed Jackson networks with single class customers and single server nodes (Cao (1987a)). This paper extends the above results to systems with finite buffer sizes. It is proved that in an indecomposable network with finite buffer sizes a perturbation will, with probability 1, be realized or lost. For systems in which no server can directly block more than one server simultaneously, the elasticity of the expected throughput can be expressed in terms of the steady state probability and the realization probability in a simple manner. The elasticity of the throughput when each customer’s service time changes by the same amount can also be calculated. These results provide some theoretical background for perturbation analysis and clarify some important issues in this area.

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