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Show the formula for Lq for an M/G/1 system simplifies to the formula for an M/M/1...

Show the formula for Lq for an M/G/1 system simplifies to the formula for an M/M/1 when G is exponential distribution (G=M)

Solutions

Expert Solution

For M/G/1 System, the Pollazcek _ khintichine Formula gives:

                                        (1)

For M/M/1syatem, when G is Exponential Distribution (G=M,

the Service Time T follows Exponential Distribution with parameter .

So, we get:

and

                                      (2)

Substituting (2), equation (1), becomes:

                                         (3)

Since

                                                    (4)

Substituting (4), equation (3) becomes:

i.e.,

i.e.,

This is the formula for an M/M/1 system.

Thus, we have shown the formula for Lq for M/G/1 system simplifies to the formulafor an M/M/1 when G is exponential distribution (G = M)

orchestra answered 1 year ago
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