### 1. Introduction

### 2. Hypothesis on Handover and New Call Ratio

*λ*

*), the handover call arrival rate (*

_{n}*λ*

*), and the average channel departure rate (*

_{h}*μ*) is essential for determining the new CBP and handover CDP. Here, it is considered that

*P*

*and*

_{B}*P*

*represent the new CBP and handover CDP, respectively. The call arriving processes are considered as Poisson’s distribution. A new call that arrives in the system may be either completed within the original cell or handed over to another cell before completing the call. The probability of a call being handed over depends on two factors: (i) the average dwell time (*

_{D}*1/η*) and (ii) the average call duration (

*1/μ*). Both the average call duration and the cell dwell time are assumed to be exponential [2,13]. The handover probability,

*P*

*, of a call at a particular time is given by:*

_{h}### 3. Conventional Guard Channel Schemes

### 3.1 Fixed Guard Band Scheme

*G*

*) entirely for handover calls among the*

_{C}*C*channels in a cell. The rest of the

*M*(=

*C – G*

*) channels are shared by both new calls and handover calls without priority. A new call is blocked if the progressive call is in state*

_{C}*M*or is more than that. A handover call is blocked if no channel is accessible in the target cell, which means that the operating state is at state

*C*. The state

*i*(

*i =*0, 1, . . . ,

*C*) of a cell is defined as the number of calls in progress. Let,

*P*(

*i*) be the steady-state probability when the system is in state

*i*. The probabilities,

*P*(

*i*), can be established by analyzing the typical birth–death processes of one-dimensional Markov chain [13].

*1/μ*). From this figure, the state balance equations can be equated as:

*λ*

*and*

_{n}*λ*

*denote the call arrival rates of new calls and handover calls, respectively. The steady-state probability,*

_{h}*P*(

*i*), is found as:

*P*

*, for a new call is given by:*

_{B}*P*

*, is given by:*

_{D}*M*to

*C*are the guard bands that only accept the handover calls.

### 3.2 Fractional Guard Channel Scheme

*P*(

*j*), is found as:

*P*

*, for a new call is given by:*

_{B}*P*

*, is given by:*

_{D}*α*denotes the acceptance factor and

*i*denotes the current state. So,

*α*

*denotes the acceptance factor of the current state. In this scheme,*

_{i}*α*

_{0}= 1,

*α*

*= 0 and the others vary randomly between 0 and 1.*

_{C}**rand**(0,1) is initiated. It can randomly produce any rational number between 0 and 1 on the basis of occupied channels that accept calls at that ratio and reject the rest of the calls.

##### Algorithm 2

### 3.3 Limited Fractional Channel Scheme

*C*channels for the LFC scheme. As the name suggests, the LFC scheme is a simplification of the more general FGC scheme, which was described earlier. In the LFC scheme, when the system is in state

*M*, new calls are accepted with the probability

*α*. From states

*M*+1 to

*C*, only handover calls are accepted and from states 0 to

*M-*1, both types of calls are accepted. Thus, the randomization in the LFC scheme is restricted to just one state as compared to the FGC scheme, where randomization could potentially occur at every state.

*α*

*=*

_{m+1}*α,*and the values of

*α*

_{i}*=*1, 0 ≤

*i*≤

*M*, and

*α*

_{i}*=*0,

*M+*1

*< i*≤

*C*.

*M*this value is 1 and from

*M+*1 to

*C*this value is 0. Only the acceptance factor for state

*M*to

*M+*1 is applicable with some defined values.

##### Algorithm 3

### 3.4 Uniform Fractional Channel Scheme

*α*, which is independent of channel occupancy, to accept new calls. The state transition rate diagram is shown in Fig. 4. This policy accepts handover calls as long as channels are available. This policy can be obtained from the FGB scheme by setting

*α*

*=*

_{k}*α*, (for

*k*= 0, 1, 2, ….

*, C–*1). The UFC scheme reserves a non-integral number of guard channels for handover calls by rejecting new calls with some probability. According to the studies given in [9,14,15] show that the UFC scheme has a lower blocking probability for new calls in a low handover and new calls traffic ratio.

*P*(

*i*), is found as:

*P*(0) can be calculated by the equation and is given as:

**rand**(0, 1) is also initiated, which randomly produces a uniform acceptance factor regardless the channel occupancy. By this technique, it is different from the FGC scheme.

##### Algorithm 4

### 4. Uniform Fractional Band Schemes

*M*in Fig. 5, new calls, and handover calls have no priority to access. When the states up to

*M*are occupied, the new calls are accepted by the states from

*M+*1 to

*N*, with a uniform acceptance factor of α. This acceptance factor is independent of the channel occupancy through the band. This type of priority is known as a fractional priority. The states from

*N+*1 to C are reserved only for handover calls like the FGB scheme. This means that these states or the corresponding set of channels accept only handover calls. Hence, the acceptance factors throughout the band for new calls are void. The priority of handover calls given by this band is called integral priority.

*M*, all new calls are accepted, but from states

*M*to

*N,*new calls are accepted by a predefined acceptance ratio. For the integral priority band from states

*N*to

*C*the channels are reserved only for handover calls, which means these channels block all new calls.

*P*(

*i*) is calculated by:

##### (16)

*P*(0) can usually be calculated by (13). Moreover, the new CBP and handover CDP are given by (17) and (18), respectively:

**rand**() produces any rational number between 0 and 1 on the basis of the predefined rate and this acceptance factor is only initiated for a band of channels. This acceptance factor works for channels

*M*to

*N*.

##### Algorithm 5

### 5. Performance Investigation

*C=*100, the guard band for the FGB scheme and for the LFC scheme,

*M=*90, and in our proposed scheme,

*N=*94. The new call arrival rate is considered from 0 to 6 calls per second in every case. Since in [6–11] the handover call rate is considered to be a fixed ratio of the new call arrival rate, comparing their results with our proposed scheme, the handover call rate is considered to be 1/6 of the new call arrival rate in every simulation. The mean call holding time,

*1/μ*, is considered for both new calls and handover calls as 90 seconds. To compute the call handover probability mean dwell time,

*1/η=*360 second.