An Approximation Method for Tandem Queues with Blocking

@article{Brandwajn1988AnAM,
  title={An Approximation Method for Tandem Queues with Blocking},
  author={Alexandre Brandwajn and Lily Jow},
  journal={Oper. Res.},
  year={1988},
  volume={36},
  pages={73-83}
}
We propose an approximate analysis of open systems of tandem queues with blocking caused by finite buffers between servers. Our approach relies on the use of marginal probability distributions (“state equivalence”) coupled with an approximate evaluation of the conditional probabilities introduced through the equivalence. The method iterates over consecutive pairs of servers using the solution of a two-queue system as a building block. It produces performance measures for individual servers as… 
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Approximate analysis of open networks of queues with blocking: Tandem configurations
TLDR
An approximation procedure is developed for the analysis of tandem configurations consisting of single server finite queues linked in series and gives results in the form of the marginal probability distribution of the number of units in each queue of the tandem configuration.
An Approximation Method for Queues in Series with Blocking
Approximation Analysis of Open Acyclic Exponential Queueing Networks with Blocking
TLDR
An iterative procedure for approximating the marginal occupancy probabilities for each queue of the system is offered, based upon the SIMP approximation previously used for tandem queues.
On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach
Control of a tandem queue with a startup cost for the second server
TLDR
This work presents a rather intuitive, easy to understand, and at the same time very accurate technique to approximate the optimal decision policy and shows that the approximation works extremely well for a wide range of parameter combinations.
A Note on Approximate Iterative Solution of Open Tandem Networks with Blocking
Product Form Approximations for Queueing Networks with Multiple Servers and Blocking
TLDR
It is shown that the equilibrium-state probabilities for this type of blocking queuing network have an approximate product-form solution, which is based on normalizing the infeasible states that violate station capacities, and the throughputs of both systems are approximately equal.
Control of a tandem queue with a startup cost for the second server
TLDR
This work presents a rather intuitive, easy to understand, and at the same time very accurate technique to approximate the optimal decision policy for tandem queues and shows that the approximation works extremely well for a wide range of parameter combinations.
Analysis and Approximation of Dual Tandem Queues with Finite Buffer Capacity
TLDR
It is shown that in general system service rate of a dual tandem queue with finite buffer capacity is equal or smaller than its bottleneck service rate, and virtual interruptions, which are the extra idle period at the bottleneck caused by the non-bottlenecks, depend on arrival rates.
Approximate Analysis of Tandem Blocking Queueing Networks with Correlated Arrivals and Services
TLDR
The accuracy of the approximation is examined and it is confirmed that the method well approximates the performance of tandem queueing networks with correlated arrivals and services.
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References

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Approximate analysis of open networks of queues with blocking: Tandem configurations
TLDR
An approximation procedure is developed for the analysis of tandem configurations consisting of single server finite queues linked in series and gives results in the form of the marginal probability distribution of the number of units in each queue of the tandem configuration.
Approximate analysis of exponential tandem queues with blocking
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