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We develop an analytical approach to the performance analysis and optimization of wireless cellular networks for which different types of calls are prioritized based on a channel reservation scheme. We assume that the channel occupancy time differs for new and handover calls. We obtain simple formulas for calculating quality of service (QoS) metrics and solve some problems related to finding the optimal values of guard channels as well as present the results of numerical experiments.

In wireless cellular networks, when a subscriber crosses the boundary of a cell (while on a call), the subscriber releases this cell’s channel and requests an empty channel in a neighboring cell. This process is called a handover. If a neighboring cell has at least one empty channel, then such a handover call (

There are various prioritization schemes for

In this paper, we consider a model with call admission control (CAC) based on guard channels schemes (GC schemes) and without queuing of

In this paper, we develop an analytical approach to the calculation of models without

In this paper, we develop an analytical approach for calculating models of a wireless network with nonidentical channel occupancy times for

Even though we consider a monoservice network for the sake of simplifying both our models and any intermediate calculations, the results that we achieve can be easily adapted for multiservice networks.

This paper is organized as follows. In Section

First, we will analyze the model of a cell belonging to a homogeneous wireless network with a CAC based on the CGC scheme. Henceforth, a homogeneous network is defined as one for which the traffic parameters of all cells within the network are statistically identical; that is, we can study the function of a representative cell in isolation. This assumption is true for practically all networks with small cells (e.g., networks with microcells).

The representative cell contains

The distribution functions corresponding to the channel occupancy times of both types of calls are exponential, but their parameters differ by the intensity of handling of

The abovementioned channel occupancy times are defined not only in terms of required service times for different call types but also in terms of the subscriber mobility within cells. In all existing works, it has been assumed that the required service times of

Cell functionality is described by a two-dimensional Markov chain (MC); that is, the state of the given system at an arbitrary moment in time is described by a two-dimensional vector

Let us denote the stationary probability of state

Henceforth, let

We should note that for practical networks, this SGEE has large dimension, which explains why its exact solution is computationally difficult. In [

Calculate the following parameters:

Calculate the approximate values of the QoS metrics in (

In the above algorithm, the following notation is used:

The authors in [

The authors noted that it is impossible to measure the accuracy of their proposed formulas analytically; therefore, they demonstrated the high accuracy of these formulas with simulations.

Another way of transforming a two-dimensional model to an approximate one-dimensional model proceeds by replacing different average channel occupation times with the weighted average

The authors in [

Tables

Comparison of different algorithms for the case

[ | [ | Traditional | [ | [ | Traditional | |

1 | 0.7310586 | 0.7746003 | 0.8374876 | |||

2 | 0.4621171 | 0.4891989 | 0.5577866 | |||

3 | 0.2516532 | 0.2588479 | 0.2998047 | |||

4 | 0.1163676 | 0.1153544 | 0.1327018 | |||

5 | 0.0453591 | 0.0435004 | 0.0492806 | |||

6 | 0.0149759 | 0.0140255 | 0.0156344 | |||

7 | 0.0042446 | 0.0039216 | 0.0043088 | |||

8 | 0.0010474 | 0.0009644 | 0.0010449 | |||

9 | 0.0002249 | 0.0002101 | 0.0002227 |

Comparison of different algorithms for the case

[ | [ | Traditional | [ | [ | Traditional | |

1 | 0.73105860 | 0.77460030 | 0.7035873 | |||

2 | 0.46211714 | 0.48919887 | 0.42770452 | |||

3 | 0.25165324 | 0.25884799 | 0.22508059 | |||

4 | 0.11636757 | 0.11535437 | 0.10127703 | |||

5 | 0.04535909 | 0.04350037 | 0.03875433 | |||

6 | 0.01497587 | 0.01402552 | 0.01267733 | |||

7 | 0.00424458 | 0.00392164 | 0.00358918 | |||

8 | 0.00104741 | 0.00096442 | 0.00089234 | |||

9 | 0.00022489 | 0.00021005 | 0.00019732 |

Comparison of different algorithms for the case

[ | [ | Traditional | [ | [ | Traditional | |

1 | 0.73105860 | 0.77460030 | 0.7746003 | |||

2 | 0.46211714 | 0.48919887 | 0.48919887 | |||

3 | 0.25165324 | 0.25884799 | 0.25884799 | |||

4 | 0.11636757 | 0.11535437 | 0.11535437 | |||

5 | 0.04535909 | 0.04350037 | 0.04350037 | |||

6 | 0.01497587 | 0.01402552 | 0.01402552 | |||

7 | 0.00424458 | 0.00392164 | 0.00392164 | |||

8 | 0.00104741 | 0.00096442 | 0.00096442 | |||

9 | 0.00022489 | 0.00021005 | 0.00021005 |

In this method, as in the CGC scheme, an

The stationary distribution of state probabilities is defined by solving the appropriate SGEE. The solution of an SGEE again presents problems with exact calculation for high-dimensional state spaces (

Here, we offer strict analysis of these formulas; moreover, we will prove that the formulas are exact if the system satisfies the local balance condition.

In the FGC scheme, as in the CGC scheme, the cell state at any time is described by a bidimensional vector

Because the loss probability of an

Let us denote the probability of the merged state

Thus,

Then, the initial QoS metrics from (

Hence, to calculate the QoS metrics in (

If the system satisfies the local balance condition, then the merged state probabilities are defined as follows:

The proof is provided in the appendix.

Thus, taking (

By applying these formulas to the special cases, we obtain exact formulas for the QoS metrics (

Note that closed-form solutions (

The problem of how to provide a given level of handling quality for different call types is scientifically and practically very interesting. The solution of such problems requires some regulated parameters. Thus, in some networks, for which the distribution of channels between cells is fixed, only call admission control parameters can be regulated because controlling loads present a difficult task and one that is sometimes practically impossible.

It is extremely difficult to develop a method for finding the optimal parameter values for the FGC scheme, as this strategy contains a large number (exactly

First, we will study the problem of organizing the fair handling of different call types. As stated above, as

However, in real life, absolutely fair handling is not required, and so we may choose to introduce the concept of

Considering that

Solutions for the problem (

10 | 10 | 10 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | |

10 | 10 | 10 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | |

2/3 | 2/3 | 2/3 | 2/3 | 2/3 | 2/3 | 2 | 2 | 2 | 2 | |

0.4 | 0.3 | ≤0.2 | 0.2 | 0.3 | 0.4 | 0.4 | 0.3 | 0.2 | ≤0.1 | |

8 | 9 | 10 | 16 | 13 | 11 | 13 | 15 | 17 | 20 |

Now let the QoS for different call types be measured by the limit values of the loss and blocking probabilities; that is, the limitations for their upper bounds are set as follows:

Then, the optimization problem is formulated as follows: find the extreme values of the parameter

Given the monotonicity of

If

If

If

If

Note that the dichotomy method can be used to solve the problem in Step

A similar method is developed for solving the following problem:

Combining the solutions of problems (

Solutions for the problem (

0.1 | 0.1 | 0.1 | 0.1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1.0 | |

4/3 | 4/3 | 4/3 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 2.0 | |

10^{−2} | 10^{−2} | 10^{−2} | 10^{−2} | 10^{−3} | 10^{−3} | 10^{−3} | 10^{−3} | 10^{−3} | 10^{−3} | |

10^{−4} | 10^{−5} | 10^{−6} | 10^{−3} | 10^{−4} | 10^{−5} | 10^{−6} | 10^{−7} | 10^{−8} | 10^{−7} | |

[ | [ | [ | [ | [ | [ | [ | [ |

It is possible to pose other similar QoS optimization problems; however, due to space limitations, they are not considered here.

We have provided exact and simple formulas for the calculation and optimization of QoS metrics for traditional wireless network models, assuming that the two fundamentally different types of calls (new and handover) do not have identical channel occupancy times. It is important to note that the adaptation of the proposed approach for next generation networks is straightforward.

To prove the above-mentioned proposition, we must first prove the following lemmas.

If the system satisfies the local balance condition, then the following equations hold:

If the system satisfies the local balance condition, then the following equations hold:

We use a technique proposed in [

Summing over the parts of the equation in Lemma

Consequently, from Lemma

Now let us suppose that the system does not satisfy the local balance condition; one can use the following approach. Taking into account the relations in (

For notational simplicity, we assume that the states

Now, various schemes may be used for the unification of channel occupancy times. If we use the heuristic from [

By using the proof schemes from our lemmas, we conclude that right side of (

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant no. 2010-0003269).