Single server Markovian feedback queueing network with shared buffer and multi-queue nodes

2020 ◽  
Author(s):  
S. Shanmugasundaram ◽  
S. Vanitha
Keyword(s):  
Queueing Network ◽  
Single Server ◽  
Shared Buffer

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.

Dynamic Scheduling of a Four-Station Queueing Network

1990 ◽  
Vol 4 (1) ◽  
pp. 131-156 ◽  
Author(s):  
C. N. Laws ◽  
G. M. Louth
Keyword(s):  
Control Problem ◽  
Dynamic Scheduling ◽  
Dynamic Control ◽  
Queueing Network ◽  
Single Server ◽  
Scheduling Policies ◽  
Resource Pooling ◽  
Static Scheduling ◽  
Open Queueing Network ◽  
Dynamic Policy

This paper is concerned with the problem of optimally scheduling a multiclass open queueing network with four single-server stations in which dynamic control policies are permitted. Under the assumption that the system is heavily loaded, the original scheduling problem can be approximated by a dynamic control problem involving Brownian motion. We reformulate and solve this problem and, from the interpretation of the solution, we obtain two dynamic scheduling policies for our queueing network. We compare the performance of these policies with two static scheduling policies and a lower bound via simulation. Our results suggest that under either dynamic policy the system, at least when heavily loaded, exhibits the form of resource pooling given by the solution to the approximating control problem. Furthermore, even when lightly loaded the system performs better under the dynamic policies than under either static policy.

scholarly journals Utility Optimization in Congested Queueing Networks

2011 ◽  
Vol 48 (1) ◽  
pp. 68-89 ◽  
Author(s):  
N. S. Walton
Keyword(s):  
Queueing Networks ◽  
Packet Switching ◽  
Queueing Network ◽  
Capacity Constraints ◽  
Switching Network ◽  
Single Server ◽  
Service Capacity ◽  
Asymptotic Regime ◽  
Utility Optimization ◽  
Aggregate Utility

We consider a multiclass single-server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of congestion controls, we analyse a sequence of stationary queueing networks. In this asymptotic regime, the service capacity of the network remains constant and the sequence of congestion controllers act to exploit the network's capacity by increasing the number of packets within the network. We show that the stationary throughput of routes on this sequence of networks converges to an allocation that maximises aggregate utility subject to the network's capacity constraints. To perform this analysis, we require that our utility functions satisfy an exponential concavity condition. This family of utilities includes weighted α-fair utilities for α > 1.

scholarly journals A queueing network analysis of dynamic reconfigurability in a hierarchical information network

1994 ◽  
Vol 31 (A) ◽  
pp. 99-114
Author(s):  
U. Narayan Bhat ◽  
Richard E. Nance
Keyword(s):  
Network Model ◽  
Network Architecture ◽  
Communication Systems ◽  
Queueing Network ◽  
Hierarchical Level ◽  
Information Network ◽  
Single Server ◽  
Computer Communication ◽  
Embedded Computer ◽  
Poisson Arrivals

Hierarchical information networks are important in applications where the information management must support an existing tree-structured organization. Embedded computer-communication systems in military applications, with a dominant hierarchical command structure, are the most prominent examples. Also typical of such applications is the variability in message demand (both sources and intensity) depending on the external conditions encountered by the encapsulating system (the system supported by the embedded computer-communication system). Using a queueing network model for a hierarchical information network, we compare the effect of limited dynamic reconfiguration on expected transmission delays. The limited reconfigurability takes the form of apex transition among a proper subset of the communication nodes designated as the apex candidate set. Each apex candidate can assume the ultimate position under designated conditions. This network architecture is called a dynamic hierarchy. The model includes N + 1 nodes (0, …, N) with 0 identifying the apex node. We assume that message processing at each node is described by an M/M/1 model (single server with Poisson arrivals and exponential service times). Further message transfers among the nodes are served by communication links which also behave as M/M/1 queues.Two distinctive features characterize the queueing network model:1. The assignment of a set of weights to the nodes dependent on the hierarchical level reflects the increasing importance of information as it is transferred to higher levels.2. The dynamic hierarchy requires a communications protocol that partitions the analysis of network delay into three periods: regular operation, reconfiguration, and adjustment. Characterization of the performance of the dynamic hierarchy entails the description of message transmission delay as a composite of the three periods.

scholarly journals Heavy-traffic approx­imations for a layered network with limited resources

2018 ◽  
Vol 37 (2) ◽  
pp. 498-532
Author(s):  
Angelos Aveklouris ◽  
Maria Vlasiou ◽  
Jiheng Zhang ◽  
Bert Zwart
Keyword(s):  
Resource Sharing ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Limited Resources ◽  
Single Server ◽  
Processor Sharing ◽  
Bottleneck Node ◽  
General Distributions ◽  
Heavy Traffic Approximations ◽  
Number Of Customers

HEAVY-TRAFFIC APPROXIMATIONS FOR A LAYERED NETWORK WITH LIMITED RESOURCESMotivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the interarrival and the service times have general distributions. Customers are served according to their arrival order at each node and after finishing their service they can re-enter at nodes several times for another service. At the second layer, active servers act as jobs that are served by a single server working at speed one in a processor-sharing fashion. We further assume that the degree of resource sharing is limited by choice, leading to a limited processor-sharing discipline. Our main result is a diffusion approximation for the process describing the number of customers in the system. Assuming a single bottleneck node and studying the system as it approaches heavy traffic, we prove a state-space collapse property.

scholarly journals Analysis of Closed Queueing Networks with Batch Service

2020 ◽  
Vol 20 (4) ◽  
pp. 527-533
Author(s):  
Elena P. Stankevich ◽  
◽  
Igor E. Tananko ◽  
Vitalii I. Dolgov ◽  
◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Queueing Networks ◽  
Manufacturing Systems ◽  
Queueing Network ◽  
Transport Systems ◽  
Batch Service ◽  
Single Server ◽  
Closed Queueing Networks ◽  
Number Of Customers

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy. The batсh service time is exponentially distributed. After a batсh finishes its execution at a node, each customer of the batch, regardless of other customers of the batch, immediately moves to another node in accordance with the routing probability. This article presents an analysis of the queueing network using a Markov chain with continuous time. The qenerator matrix is constructed for the underlying Markov chain. We obtain expressions for the performance measures. Some numerical examples are provided. The results can be used for the performance analysis manufacturing systems, passenger and freight transport systems, as well as information and computing systems with parallel processing and transmission of information.

scholarly journals Single server queueing networks with varying service times and renewal input

2000 ◽  
Vol 13 (4) ◽  
pp. 429-450 ◽  
Author(s):  
Pierre Le Gall
Keyword(s):  
Network Management ◽  
Queueing Networks ◽  
Queueing Network ◽  
Single Server ◽  
Simulation Methods ◽  
Tandem Queues ◽  
Tandem Queue ◽  
Queueing Delay ◽  
New Concepts ◽  
Service Times

Using recent results in tandem queues and queueing networks with renewal input, when successive service times of the same customer are varying (and when the busy periods are frequently not broken up in large networks), the local queueing delay of a single server queueing network is evaluated utilizing new concepts of virtual and actual delays (respectively). It appears that because of an important property, due to the underlying tandem queue effect, the usual queueing standards (related to long queues) cannot protect against significant overloads in the buffers due to some possible “agglutination phenomenon” (related to short queues). Usual network management methods and traffic simulation methods should be revised, and should monitor the partial traffic streams loads (and not only the server load).

scholarly journals Sequential scheduling of priority queues and Arm-acquiring bandits

1987 ◽  
Vol 1 (2) ◽  
pp. 115-135 ◽  
Author(s):  
Chuanshu Ji
Keyword(s):  
Optimal Policy ◽  
Average Cost ◽  
Queueing Network ◽  
Single Server ◽  
Index Policy ◽  
Discounted Cost ◽  
Poisson Arrival ◽  
Long Run ◽  
Holding Cost ◽  
Arrival Processes

In a queueing network with a single server and r service nodes, a non-preemptive non-idling policy chooses a node to service at each service completion epoch. Under the assumptions of independent Poisson arrival processes, fixed routing probabilities, and linear holding cost rates, we apply Whistle's method for Arm-acquiring bandits to show that for minimizing discounted cost or long-run average cost the optimal policy is an index policy. We also give explicit expressions for those priority indices.

scholarly journals Utility Optimization in Congested Queueing Networks

2011 ◽  
Vol 48 (01) ◽  
pp. 68-89
Author(s):  
N. S. Walton
Keyword(s):  
Queueing Networks ◽  
Packet Switching ◽  
Queueing Network ◽  
Capacity Constraints ◽  
Switching Network ◽  
Single Server ◽  
Service Capacity ◽  
Asymptotic Regime ◽  
Utility Optimization ◽  
Aggregate Utility

We consider a multiclass single-server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of congestion controls, we analyse a sequence of stationary queueing networks. In this asymptotic regime, the service capacity of the network remains constant and the sequence of congestion controllers act to exploit the network's capacity by increasing the number of packets within the network. We show that the stationary throughput of routes on this sequence of networks converges to an allocation that maximises aggregate utility subject to the network's capacity constraints. To perform this analysis, we require that our utility functions satisfy an exponential concavity condition. This family of utilities includes weighted α-fair utilities for α > 1.

Stationary Waiting Time in Parallel Queues with Synchronization

2020 ◽  
Author(s):  
Mariana Olvera-Cravioto ◽  
Octavio Ruiz-Lacedelli
Keyword(s):  
Waiting Time ◽  
Random Number ◽  
Queueing Network ◽  
Service Discipline ◽  
Single Server ◽  
Computing Systems ◽  
Parallel Queues ◽  
Server Queue ◽  
Stationary Waiting Time ◽  
Distributed Queueing

Motivated by database locking problems in today’s massive computing systems, we analyze a queueing network with many servers in parallel (files) to which jobs (writing access requests) arrive according to a Poisson process. Each job requests simultaneous access to a random number of files in the database and will lock them for a random period of time. Alternatively, one can think of a queueing system where jobs are split into several fragments that are then randomly routed to specific servers in the network to be served in a synchronized fashion. We assume that the system operates on a first-come, first-served basis. The synchronization and service discipline create blocking and idleness among the servers, which leads to a strict stability condition compared with other distributed queueing models. We analyze the stationary waiting time distribution of jobs under a many-server limit and provide exact tail asymptotics. These asymptotics generalize the celebrated Cramér–Lundberg approximation for the single-server queue.

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