Queueing networks please some experts help me

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In summary, the speaker is seeking help with evaluating the steady state behavior of queueing networks with finite buffers and a "blocking after service" policy. They are specifically interested in finding analytical treatments and expressions for calculating the effective service time of each node, particularly in the case of merge and splitting nodes. They are directed to look at certain books and their references for more information.
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Gabriele
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Queueing networks...please some experts help me!

Hello to everyone.

I have a question concerning Queuing Theory and in particular Queueing Networks. For my Ph.D thesis I need to evaluate the steady state behavior of queueing networks featuring finite buffers between nodes and "blocking after service" policy. For simplicity, I'm in the particular case in which the arrival rate and the service rate of each node can be considered "deterministic" (i.e. each node is a D/D/1 queue with finite buffer of K positions).

Now, some queueing nodes can be bottlenecks. A bottleneck in this case means that its service time is greater than its inter-arrival time yields to an utilization factor of the node higher than 1. In this case, due to the bottleneck presence, upstream nodes will be blocked and their effective service times are higher than their corresponding theoretical (ideal) ones.

I need to known where I can find some analytical threatment of such kind of networks. Especially I need to found proper expressions in order to calculate the effective service time of each node of the network, mainly in the case of merge queueing nodes (nodes with multiple in-coming connections with other nodes) and splitting stations (nodes with multiple out-going arcs and a routing probability among them).

Do you know something about this?

Thanks

Gabriele
 
Mathematics news on Phys.org

What are queueing networks and how do they work?

Queueing networks are mathematical models used to analyze the flow of data or information through a system. They consist of a series of interconnected queues, where items or customers enter the system and move through the queues based on certain rules. The goal is to understand the performance of the system and identify potential bottlenecks or areas for improvement.

What are the benefits of using queueing networks?

Queueing networks provide valuable insights into the behavior of complex systems, allowing for optimization and performance improvement. They can also help in predicting system performance under different scenarios, such as changes in demand or resource availability. Additionally, queueing networks are often used in the design and analysis of communication networks, computer systems, and manufacturing processes.

What are the key components of a queueing network?

The key components of a queueing network include the arrival process, service process, and queueing discipline. The arrival process determines how items or customers enter the system, while the service process determines how long it takes to process each item. The queueing discipline dictates the rules for how items are selected from the queue for service, such as first-in-first-out or shortest processing time.

What are some common applications of queueing networks?

Queueing networks have a wide range of applications, including traffic flow, customer service, call centers, healthcare systems, and more. They are also commonly used in operations research and industrial engineering to improve system performance and efficiency.

How are queueing networks analyzed and solved?

Queueing networks can be analyzed using mathematical models and simulation techniques. The most common methods include Markov models, queuing theory, and discrete event simulation. These methods allow for the calculation of performance metrics such as average waiting time, system throughput, and resource utilization, which can then be used to optimize the system.

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