Energy-Aware M^X/G/1 Queue

mean arrival rate of batches

0.2

max idling time

1000

mean batch size

2

setup delay

0

simulation time

5000

mean number of jobs	=	1.15127
mean time in the system	=	2.93049 s
mean power consumption	=	149.355 W

In queueing theory, an

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/

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/1 queue (in Kendall notation) is a model in which arrivals satisfy a Markovian distribution

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, service times have an unknown distribution, called a general distribution

G

, and there is a single server. Additional notation: PS indicates that there is processor sharing on the server, while

X

M

indicates that the arrival distribution is batch Markovian with a random number

X

of simultaneous arrivals.

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M

/

G

/1-PS queueing systems are well-known models in the performance analysis of various systems, ranging from telecommunication channels to air transportation systems. Consider an energy-aware

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/

G

/1-PS system, which may possibly be put in a sleep state to save energy whenever it is idle. In most cases, such a system needs some setup time before it "wakes up" from a sleep state to process requests. This Demonstration illustrates how the number of requests of such a system evolve through time. Statistics for mean values are provided in the lower panel.