scholarly journals Monotonicity of throughput in non-Markovian networks

1989 ◽  
Vol 26 (01) ◽  
pp. 134-141 ◽  
Author(s):  
Pantelis Tsoucas ◽  
Jean Walrand
Keyword(s):  
Queueing Networks ◽  
Buffer Size ◽  
Waiting Room ◽  
Finite Buffers ◽  
Closed Network ◽  
Markovian Queueing Networks

Monotonicity of throughput is established in some non-Markovian queueing networks by means of pathwise comparisons. In a series of · /GI/s/N queues with loss at the first node it is proved that increasing the waiting room and/or the number of servers increases the throughput. For a closed network of · /GI/s queues it is shown that the throughput increases as the total number of jobs increases. The technique used for these results does not apply to blocking systems with finite buffers and feedback. Using a stronger coupling argument we prove throughput monotonicity as a function of buffer size for a series of two ·/M/1/N queues with loss and feedback from the second to the first node.

Some distributional approximations in Markovian queueing networks

1982 ◽  
Vol 14 (03) ◽  
pp. 654-671 ◽  
Author(s):  
T. C. Brown ◽  
P. K. Pollett
Keyword(s):  
Queueing Networks ◽  
Poisson Processes ◽  
Single Class ◽  
Open Network ◽  
State Dependent ◽  
Service Rates ◽  
Distributional Approximations ◽  
Closed Network ◽  
Poisson Approximations ◽  
Markovian Queueing Networks

We consider single-class Markovian queueing networks with state-dependent service rates (the immigration processes of Whittle (1968)). The distance of customer flows from Poisson processes is estimated in both the open and closed cases. The bounds on distances lead to simple criteria for good Poisson approximations. Using the bounds, we give an asymptotic, closed network version of the ‘loop criterion' of Melamed (1979) for an open network. Approximation of two or more flows by independent Poisson processes is also studied.

Overall station balance and decomposability for non-Markovian queueing networks

1998 ◽  
Vol 30 (03) ◽  
pp. 870-887 ◽  
Author(s):  
D. Fakinos ◽  
A. Economou
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Necessary And Sufficient Conditions ◽  
Jackson Type ◽  
Necessary And Sufficient ◽  
Markovian Queueing Networks

Introducing the concept of overall station balance which extends the notion of station balance to non-Markovian queueing networks, several necessary and sufficient conditions are given for overall station balance to hold. Next the concept of decomposability is introduced and it is related to overall station balance. A particular case corresponding to a Jackson-type queueing network is considered in some more detail.

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