Probabilty of waiting in M/M/C

[Minseok Oh]

Hi,

I am trying to convince myself that the the probability of waiting, 1
- Wq(0) in M/M/C approaches to 1 as r -> infinity under efficiency
domain. That is, rho = r / c approaches to 1 (rho is always less than
1)

1 - Wq(0) = r^c / [c! (1 - rho)] / { r^c / [c! (1 - rho)] + sum_from
n=0 to c - 1 r^n / n! }

I can't find the limit which is clamed to be close to 1 as r
increases.

Please help me on this.

Thank you in advance.

Regards,

Minseok

[A. ÜLKER]

Can you wait for the answer? Little busy today.

2011/1/16 Minseok Oh <msoh...@gmail.com>

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"Matematiğin hiçbir alanı yoktur ki nekadar soyut olursa olsun bir gün gerçek dünyada uygulama alanı bulmasın."
"There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world."  Lobachevsky

Alper ÜLKER

Ağrı İ.Ç. Üniversitesi

Fen-Edebiyat Fakültesi

Matematik Bölümü

[Minseok Oh]

No problem. Thanks.

On Jan 16, 9:08 pm, A. ÜLKER <alprul...@gmail.com> wrote:
> Can you wait for the answer? Little busy today.
>

> 2011/1/16 Minseok Oh <msohm...@gmail.com>

>
>
>
>
>
> > Hi,
>
> > I am trying to convince myself that the the probability of waiting, 1
> > - Wq(0) in M/M/C approaches to 1 as r -> infinity under efficiency
> > domain. That is, rho = r / c approaches to 1 (rho is always less than
> > 1)
>
> > 1 - Wq(0) = r^c / [c! (1 - rho)] / { r^c / [c! (1 - rho)]  + sum_from
> > n=0 to c - 1 r^n / n! }
>
> > I can't find the limit which is clamed to be close to 1 as r
> > increases.
>
> > Please help me on this.
>
> > Thank you in advance.
>
> > Regards,
>
> > Minseok
>
> > --
> > You received this message because you are subscribed to the Google Groups
> > "advance in mathematics" group.
> > To post to this group, send email to aim...@googlegroups.com.
> > To unsubscribe from this group, send email to

> > aimaths+u...@googlegroups.com<aimaths%2Bunsu...@googlegroups.com­>
> > .

> > For more options, visit this group at
> >http://groups.google.com/group/aimaths?hl=en.
>
> --
> "Matematiğin hiçbir alanı yoktur ki nekadar soyut olursa olsun bir gün
> gerçek dünyada uygulama alanı bulmasın."

> *"There is no branch of mathematics, however abstract, which may not some
> day be applied to phenomena of the real world."  **Lobachevsky*
>
> *Alper ÜLKER
>
> Ağrı İ.Ç. Üniversitesi*
> *Fen-Edebiyat Fakültesi*
> *Matematik Bölümü*- Hide quoted text -
>
> - Show quoted text -