scholarly journals Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

2000 ◽  
Vol 37 (3) ◽  
pp. 890-899 ◽  
Author(s):  
José Niño-Mora ◽  
Kevin D. Glazebrook
Keyword(s):  
Stability Condition ◽  
Queueing Networks ◽  
Sufficient Conditions ◽  
Rate Condition ◽  
Multiclass Queueing Networks ◽  
Traffic Conditions ◽  
Peak Rate ◽  
Multiclass Queueing ◽  
Service Stations ◽  
The Stability

We argue the importance both of developing simple sufficient conditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu–Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.

scholarly journals Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

2000 ◽  
Vol 37 (03) ◽  
pp. 890-899 ◽  
Author(s):  
José Niño-Mora ◽  
Kevin D. Glazebrook
Keyword(s):  
Stability Condition ◽  
Queueing Networks ◽  
Sufficient Conditions ◽  
Rate Condition ◽  
Multiclass Queueing Networks ◽  
Traffic Conditions ◽  
Peak Rate ◽  
Multiclass Queueing ◽  
Service Stations ◽  
The Stability

We argue the importance both of developing simple sufficient conditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu–Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.

scholarly journals Stability of multiclass queueing networks under longest-queue and longest-dominating-queue scheduling

2016 ◽  
Vol 53 (2) ◽  
pp. 421-433 ◽  
Author(s):  
Ramtin Pedarsani ◽  
Jean Walrand
Keyword(s):  
Queueing Networks ◽  
Robust Scheduling ◽  
Scheduling Policy ◽  
Multiclass Queueing Networks ◽  
Open Networks ◽  
Throughput Optimality ◽  
Multiclass Queueing ◽  
Queue Scheduling ◽  
Service Rates ◽  
The Stability

Abstract We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routeing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The arrival and potential service processes and routeing decisions at the queues are independent, stationary, and ergodic. A scheduling policy is called robust if it does not depend on the arrival and service rates nor on the routeing probabilities. A policy is called throughput-optimal if it makes the system stable whenever the parameters are such that the system can be stable. We propose two robust policies: longest-queue scheduling and a new policy called longest-dominating-queue scheduling. We show that longest-queue scheduling is throughput-optimal for two groups of two queues. We also prove the throughput-optimality of longest-dominating-queue scheduling when the network topology is acyclic, for an arbitrary number of groups and queues.

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