Modeling and Performance Analysis of an Improved Data Channel Assignment (DCA) Scheme for 3G/WLAN Mixed Cells

Abstract

In this paper, we present an efficient data channel assignment (DCA) scheme for a mixed cell (i.e., a 3G cell with embedded WLANs). Our effort is essential to increase the data request (i.e., a call) handling capacity in 3G systems, with a ‘low request dropping probability’. In UMTS-first DCA scheme prefers 3G channel in dual coverage and reduces vertical handoffs from 3G to WLAN. But it deprives some users of high speed service of WLAN even when WLAN facility is available. On the contrary, a WLAN-first DCA scheme overcomes this problem by preferring WLAN system. But the overall call request dropping probability increases with increasing WLAN traffic and at some point, the benefit of WLAN cannot be achieved in a mixed cell. Further, most of the existing models do not consider the reality of non-identical WLAN-hotspots and bidirectional vertical handoffs, restricting the free mobility of the users across 3G and WLAN systems. We propose an improved DCA scheme based on WLAN-first access technique to maximize the usage of WLAN. The proposed model considers the reality of non-identical WLAN-hotspots and allows free mobility between 3G and WLAN. A proposed DCA scheme improves the dropping probability as blocked call request of WLAN are transferred to 3G. Our DCA scheme drops a request only when all the channels of both 3G and WLAN systems are busy. We derive an analytical model for proposed scheme and validate the same with a set of simulation results. We provide an extensive number of numerical results to show that our scheme performs far better than the existing models. The DCA modeling approach can be quite conveniently used for better planning of WLAN hotspots in the mixed cell.

Appendices

Appendix 1

$$p = \frac{{\mathop \sum \nolimits_{w = 1}^{W} A^{w} }}{{A_{ttl}^{H} \left( {1 - \frac{1}{d}} \right) + \left( {\frac{{A^{u} }}{d}} \right)}}$$

Proof

Say, there are $H$ hotspots and $W$ WLAN-hotspots in a mixed cell. The area of any $ith$ hotspot is $A_{i}^{H}$ and $wth$ WLAN-hotspot is $A^{w}$. Coverage area of a UMTS cell is ${\text{A}}^{\text{u}}$. According to the definition of density ratio we write,

$$d = \frac{WLAN - hotspot users per unit area}{Non - hotspot users per unit area}$$

Or,

$$d = \frac{{d^{w - h} }}{{d^{non - h} }} = \frac{{\left( {\frac{WLAN - hotspot users}{{\mathop \sum \nolimits_{w = 1}^{W} A^{w} }}} \right)}}{{\frac{ Non - hotspot users}{{A^{u} - \mathop \sum \nolimits_{i = 1}^{H} A_{i}^{H} }}}} = \frac{{\left( {A^{u} - \mathop \sum \nolimits_{i = 1}^{H} A_{i}^{H} } \right)}}{{\mathop \sum \nolimits_{w = 1}^{W} A^{w} }}.\frac{WLAN hotspot users}{Non - hotspot users}$$

where ${\text{d}}^{{{\text{w}} - {\text{h}}}}$ is number of users per unit area in hotspots (WLAN or WLAN-less) ${\text{d}}^{{{\text{non}} - {\text{h}}}}$ is number of users per unit area of non-hotspot regions.

$$Non - hotspot user = \frac{{\left( {A^{u} - \mathop \sum \nolimits_{i = 1}^{H} A_{i}^{H} } \right)}}{{d\mathop \sum \nolimits_{w = 1}^{W} A^{w} }} \times WLAN - hotspot users$$

(41)

$$\begin{aligned} \frac{WLAN - less hotspot users}{WLAN - hotspot users} = & \frac{{dd^{non - h} \left\{ {\left( {\mathop \sum \nolimits_{i = 1}^{H} A_{i}^{H} } \right) - \left( {\mathop \sum \nolimits_{w = 1}^{W} A^{w} } \right)} \right\}}}{{dd^{non - h} \mathop \sum \nolimits_{w = 1}^{W} A^{w} }} \\ = WLAN - less hotspot users = \frac{{\mathop \sum \nolimits_{i = 1}^{H} A_{i}^{H} - \mathop \sum \nolimits_{w = 1}^{W} A^{w} }}{{\mathop \sum \nolimits_{w = 1}^{W} A^{w} }} \times WLAN - hotspot users \\ \end{aligned}$$

(42)

From the definition of ${\mathbf{P}}_{\text{c}}$ we write,

$$\begin{aligned} P = & \frac{WLAN - hotspot users}{Mixed Users} \\ = \frac{WLAN - hotspot users}{non - hotspot users + WLAN - hotspot users + WLAN - less - hotspot users} \\ \end{aligned}$$

(43)

Applying Eqs. (41) and (42) in Eq. (43), we get,

$$P = \frac{{\mathop \sum \nolimits_{w = 1}^{W} A^{w} }}{{A_{ttl}^{H} \left( {1 - \frac{1}{d}} \right) + \left( {\frac{{A^{U} }}{d}} \right)}}$$

(44)

where $A_{total}^{H} = \sum\nolimits_{i = 1}^{H} {A_{i}^{H} }$ i.e., total area of all hotspots.

If all hotspots are identical then from Eq. (44) we easily prove that,

$$P = \frac{W}{{H\left( {1 - \frac{1}{d}} \right) + \left( {\frac{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 A}}\right.\kern-0pt} \!\lower0.7ex\hbox{$A$}}}}{d}} \right)}}$$

where $A = A^{w} /A^{u} .$

Appendix 2

$$\lambda_{vr}^{u} = b\prime P_{n}^{w} \lambda_{n}^{W - t} + b\prime P_{vr}^{w} \lambda_{vr}^{W - t}$$

$$\begin{aligned} \lambda_{vr}^{u} = \mathop \sum \limits_{w = 1}^{W} \lambda_{vr}^{u\left( w \right)} = & \mathop \sum \limits_{w = 1}^{W} \left( {(b^{w} )\prime P_{n}^{w} (p^{w} \lambda_{n}^{m} ) + (b^{w} )\prime P_{vr}^{w} \lambda_{vr}^{w} } \right) \\ = P_{n}^{w} \lambda_{n}^{m} \mathop \sum \limits_{w = 1}^{W} (b^{w} )\prime p^{w} + \mathop \sum \limits_{w = 1}^{W} (b^{w} )\prime P_{vr}^{w} \lambda_{vr}^{w} \\ = P_{n}^{w} \lambda_{n}^{m} \sum\nolimits_{w = 1}^{W} {(b^{w} )\prime p^{w} + P_{vr}^{w} } \sum\nolimits_{w = 1}^{W} {(b^{w} )\prime \lambda_{vr}^{w} } \\ \end{aligned}$$

Using Eq. (14a) for $\lambda_{vr}^{w}$

$$\begin{gathered} = P_{n}^{w} \lambda_{n}^{m} \sum\nolimits_{w = 1}^{W} {(b^{w} )\prime g^{w} } + P_{vr}^{w} \sum\nolimits_{w = 1}^{W} {((b^{w} )\prime g^{w} } b_{1}^{\prime } g^{w} \lambda_{n}^{u} + (b^{w} )\prime b_{2}^{\prime } g^{w} \lambda_{hr}^{u} + (b^{w} )\prime b_{2}^{\prime } g^{w} \lambda_{vr}^{u} ) \hfill \\ = P_{n}^{w} \lambda_{n}^{m} \mathop \sum \limits_{w = 1}^{W} (b^{w} )\prime g^{w} + P_{vr}^{w} b_{1}^{\prime } \lambda_{n}^{u} \mathop \sum \limits_{w = 1}^{W} (b^{w} )\prime g^{w} + P_{vr}^{w} b_{2}^{\prime } \lambda_{hr}^{u} \mathop \sum \limits_{w = 1}^{W} (b^{w} )\prime g^{w} + P_{vr}^{w} b_{2}^{\prime } \lambda_{vr}^{u} \mathop \sum \limits_{w = 1}^{W} (b^{w} )\prime g^{w} \hfill \\ = P_{n}^{w} \lambda_{n}^{m} \mathop \sum \limits_{w = 1}^{W} \left\{ {g^{w} - b^{w} g^{w} } \right\} + P_{vr}^{w} b_{1}^{\prime } \lambda_{n}^{u} \mathop \sum \limits_{w = 1}^{W} \left\{ {g^{w} - b^{w} g^{w} } \right\} + P_{vr}^{w} b_{2}^{\prime } \lambda_{hr}^{u} \mathop \sum \limits_{w = 1}^{W} \left\{ {g^{w} - b^{w} g^{w} } \right\} + P_{vr}^{w} b_{2}^{\prime } \lambda_{vr}^{u} \mathop \sum \limits_{w = 1}^{W} \left\{ {g^{w} - b^{w} g^{w} } \right\} \hfill \\ = P_{n}^{w} \lambda_{n}^{m} \left( {p - bp} \right) + P_{vr}^{w} b_{1}^{\prime } \lambda_{n}^{u} \left( {p - bp} \right) + P_{vr}^{w} b_{2}^{\prime } \lambda_{hr}^{u} \left( {p - bp} \right) + P_{vr}^{w} b_{2}^{\prime } \lambda_{vr}^{u} \left( {p - bp} \right); \hfill \\ \end{gathered}$$

where $b = (1/p)\sum\nolimits_{w = 1}^{W} {b^{w} g^{w} }$

$$\begin{gathered} = b^{{\prime }} P_{n}^{w} (p\lambda_{n}^{m} ) + P_{vr}^{w} b_{1}^{{\prime }} \lambda_{n}^{u} \left( {b^{{\prime }} p} \right) + P_{vr}^{w} b_{2}^{{\prime }} \lambda_{hr}^{u} \left( {b^{{\prime }} p} \right) + P_{vr}^{w} b_{2}^{{\prime }} \lambda_{vr}^{u} \left( {b^{{\prime }} p} \right) \hfill \\ = b{\prime }P_{n}^{w} \lambda_{n}^{W - t} + P_{vr}^{w} b^{{\prime }} \left[ {\left( {b_{1}^{{\prime }} p\lambda_{n}^{u} } \right) + \left( {b_{2}^{{\prime }} p\lambda_{hr}^{u} } \right) + \left( {b_{2}^{{\prime }} p\lambda_{vr}^{u} } \right)} \right] \hfill \\ = b{\prime }P_{n}^{w} \lambda_{n}^{W - t} + b{\prime }P_{vr}^{w} \lambda_{vr}^{W - t} \hfill \\ \end{gathered}$$

Handoff probability from WLAN to UMTS is assumed to be the same for all WLAN-hotspot and is equal to $P_{n}^{w}$ and $P_{vr}^{w}$

Appendix 3

$$K_{3} = \frac{{b^{\prime } p\left[ {P_{n}^{w} + P_{vr}^{w} \left\{ {b_{1}^{\prime } + b_{2}^{\prime } K_{1} } \right\}\left( {1 - (1 - qb)p} \right)} \right]}}{{1 - b^{\prime } P_{vr}^{w} b_{2}^{\prime } p(1 + K_{2} )}}$$

Proof

We consider the Eqs. (17), (15) and derive the following,

$$\lambda_{hr}^{u} = K_{1} \lambda_{n}^{u} + K_{2} \lambda_{vr}^{u}$$

(45)

$$\lambda_{vr}^{W - t} = b_{1}^{\prime } p\lambda_{n}^{u} + b_{2}^{\prime } p\lambda_{hr}^{u} + b_{2}^{\prime } p\lambda_{vr}^{u}$$

(46)

Since $b = (1/p)\sum\nolimits_{W = 1}^{W} {(g^{w} b^{w} )}$ or $bp = \sum\nolimits_{W = 1}^{W} {(g^{w} b^{w} )}$, From (10), we have,

$$\lambda_{n}^{u} = \left( {p\prime + qbp} \right)\lambda_{n}^{m} = \left( {1 - (1 - qb)p} \right)\lambda_{n}^{m}$$

(47)

where $q = \frac{1}{bp}\sum\nolimits_{w = 1}^{W} {q^{w} b^{w} p^{w} }$

$$\lambda_{vr}^{u} = b\prime P_{n}^{w} \lambda_{n}^{W - t} + b\prime P_{vr}^{w} \lambda_{vr}^{W - t}$$

(48)

Applying Eq. (46) in Eq. (48), we have,

$$\lambda_{vr}^{u} = b\prime P_{n}^{w} \lambda_{n}^{W - t} + b\prime P_{vr}^{w} b_{1}^{\prime } p\lambda_{n}^{u} + b\prime P_{vr}^{w} b_{2}^{\prime } p\lambda_{hr}^{u} + b\prime P_{vr}^{w} b_{2}^{\prime } p\lambda_{vr}^{u}$$

(49)

Apply Eq. (45) in (49);

$$\lambda_{vr}^{u} = b\prime P_{n}^{w} \lambda_{n}^{W - t} + b\prime P_{vr}^{w} b_{1}^{\prime } p\lambda_{n}^{u} + b\prime P_{vr}^{w} b_{2}^{\prime } pK_{1} \lambda_{n}^{u} + b\prime P_{vr}^{w} b_{2}^{\prime } pK_{2} \lambda_{vr}^{u} + b\prime P_{vr}^{w} b_{2}^{\prime } p\lambda_{vr}^{u}$$

(50)

$$\lambda_{vr}^{u} = \frac{{b\prime P_{n}^{w} }}{{1 - b^{\prime } P_{vr}^{w} b_{2}^{\prime } p(1 + K_{2} )}}\lambda_{n}^{W - t} + \frac{{b\prime pP_{vr}^{w} \left\{ {b_{1}^{\prime } + b_{2}^{\prime } K_{1} } \right\}}}{{1 - b^{\prime } P_{vr}^{w} b_{2}^{\prime } p(1 + K_{2} )}}\lambda_{n}^{u}$$

(51)

Apply Eq. (47) and $\lambda_{n}^{W - t} = p\lambda_{n}^{m}$ in Eq. (51)

$$\lambda_{vr}^{u} = \frac{{b\prime p\left[ {P_{n}^{w} + P_{vr}^{w} \left\{ {b_{1}^{\prime } + b_{2}^{\prime } K_{1} } \right\}\left( {\left( {1 - (1 - qb)p} \right)} \right)} \right]}}{{1 - b^{\prime } P_{vr}^{w} b_{2}^{\prime } p(1 + K_{2} )}}\lambda_{n}^{m}$$

$$\lambda_{vr}^{u} = K_{3} \lambda_{n}^{m}$$

where $K_{3} = \frac{{b^{'} p\left[ {P_{n}^{w}\,+\,P_{vr}^{w} \left\{ {b_{1}^{'}\,+\,b_{2}^{'} K_{1} } \right\}\left( {1 - (1 - qb)p} \right)} \right]}}{{1 - b^{'} P_{vr}^{w} b_{2}^{'} p(1 + K_{2} )}}$