Channel Allocation Schemes for Permanent User ...

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Channel Allocation Schemes for Permanent User Channel Assignment in Wireless Cellular Networks Muhammad Rehan Usman and Soo Young Shin Muhammad Rehan Usman is with the WENS Lab, Department of IT Convergence Engineering, Kumoh National Institute of Technology (KIT), South Korea (e-mail: [email protected]). Soo Young Shin is also with the WENS Lab, Department of IT Convergence Engineering, Kumoh National Institute of Technology (KIT), South Korea (Corresponding author, phone:+82-1091924998 e-mail: [email protected]).

ABSTRACT In this paper two different models for permanent user channel assignment, based on Markov chain, are proposed for wireless cellular networks. Both models include channels for calling, handover and permanent assignment. Models in this paper provide comparison of the blocking probabilities and handover failure probabilities after introducing the permanent user channel assignment, further permanent user channel blocking probability is also derived. Based on the blocking probability results, risk analysis to predict the blocked channels is provided at the end of this paper using the @ risk tool. The simulation results are provided in two parts i.e. 1) the probability curves against the number of assigned channels are shown and 2) the results using @ Risk tool for the risk analysis are shown.

Keywords: Blocking Probability, channel allocation, handovers, Markov chain, risk analysis, tele-traffic theory and wireless cellular networks

1.

INTRODUCTION

Now days in wireless cellular networks, due to increase in user traffic, different channel allocation strategies are being introduced to overcome call blocking and handover failures. To meet the growing user demand, telecommunication companies are now moving towards small cell implementations to increase the capacity of the system. Because of the huge number of mobile users there is a need of efficient resource utilization to overcome channel allocation problems in a limited spectrum [1] [2]. Cellular networks today not only accommodate normal users but also high priority users for which blocking issues are out of question (e.g. Military, Police and Emergency services etc.). Reducing the cell sizes will give rise to the number of handovers and may lead to increased call blocking and handover failure issues. This will also have a bad effect on high priority users as their blocking probabilities may increase. Call blocking and handover failure occur mostly due to unavailability of channels at the base station (BS), call blocking means newly initiated calls being blocked and handover failure refers to ongoing calls being dropped when moving from one cell to another [3]. In cellular networks, until now several different strategies have been implemented to overcome blocking issues. These are categorized into two such as; priority based and no priority based strategies. Such examples can be found in [4] and [5]. In [5] blocking probabilities have been derived

for priority and no priority based allocations. Main focus in [4] is handover blocking probability to improve the call completion rate. Handovers have key role in maintaining the quality of service (QoS) as if an ongoing call is terminated; it will have more negative impact than a new initiated call being blocked [4]. With respect to priority channel assignment some research on queuing based channel assignment strategies have also been conducted. In [6] authors have proposed a time based first come first out (FIFO) channel assignment scheme where as separate area in the cell is defined to entertain the handover users leaving and entering the cell. Similarly, in [7] a measure based priority scheme (MBPS) is proposed which is slightly different from FIFO in terms of queuing strategy, i.e., thresholds are defined for power levels, stronger the power of the portable user more chances of getting the connection first. For checking the performance of the BSs, a system model is proposed in [8] based on two dimensional Markov chain with respect to call blocking probability and handover failure in addition with channel utilization. In parallel with queuing strategies, channel borrowing has also been investigated. Channel borrowing is a simple concept, i.e., when a new call arrives or a handover occurs and all the channels of that specific cell are busy, a channel is borrowed from the neighboring cell [9]. In [10], authors have provided a channel borrowing strategy based on the pattern of the cell implementation, i.e., with compact pattern,

Template for submitting papers to IETE Journal of Research. performance is increased. Channel borrowing may be of two types, i.e., horizontal and vertical. In horizontal channel borrowing; channels are borrowed from adjacent homogeneous cells while in vertical; channels are borrowed from heterogeneous cells [11]. In [11] analysis for improving the QoS of the system is performed using horizontal and vertical channel borrowing. As mentioned earlier, we have a limited spectrum so all the channel allocation techniques or strategies are implemented under the umbrella of three main channel allocation strategies i.e. fixed channel allocation (FCA), dynamic channel allocation (DCA) and hybrid channel allocation (HCA). Description of FCA, DCA and HCA is provided in [12]. All the channel allocation schemes have provided different allocation strategies for the handovers and new calls. As mentioned earlier, in today’s cellular networks we also have high priority users (e.g. Military, Police and Emergency services etc.) for which blocking is highly undesirable. Keeping this in mind, in this paper, two new schemes have been proposed in which permanent channels have been considered for the use of high priority users. These schemes will not only focus on handover and new call blocking but will also focus on permanent channel blocking. Further using the probability values, a risk analysis is also provided using the palisade @ risk software. The software provides us the future prediction based on the historical probability values that which channels will most likely face blocking. The paper is organized in the following manner. Section II consists of the system models, Section III contains the simulation results including the risk analysis part and finally concluding remarks are provided in the section IV.

2. PROPOSED MODELS To have better understanding of the proposed models, let us begin with the Markov Chain. It is a random process to find out the probability of total states. It is usually characterized as memory less; the next state is dependent only on the current or present state but not on the sequence following the present state [13]. For example, in Fig. 1, if n is the present state then n+1 is dependent only on the nth state but not on the n-1 and previous states. Two models have been proposed in this paper based on the 2-Dimensioanl Markov Chain i.e. 1) channels are allocated in a way that only permanent users have the highest priority with reserved channels, while handovers and new calls have same priority with no reserved channels, i.e., reserved allocation for permanent assignment (RAPA) and 2) channel assignment is done in way that handovers and permanent users have high

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Figure 1. Example: Markov Chain.

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Figure 2. Markov Chain model for RAPA.

priority with reserved channels and the remaining channels are for the new calls, i.e., reserved allocation for handovers and permanent assignment (RAHPA). Further details of these models, with analytical methods, are provided in the Subsections A and B. 2.1 Reserved Allocation for Permanent Assignment In this model, we have reserved channels for permanent allocation, rest of the channels are available for newly initiated calls, permanent allocation and handovers. Although we have reserved channels for permanent allocation but still permanent users can be allocated to any channel, from the rest of the remaining channels, if all reserved ones are busy. For handovers and new calls, first come first serve policy is considered as they have the same priority. In Fig. 2 we have total 𝑎 states where, 𝜆𝑜 is the new call arrival rate, 𝜆ℎ is the handover arrival rate, 𝜆𝑝 is the permanent job arrival rate, µℎ is the handover service rate, µ𝑂 is new call service rate and µ𝑃 is permanent job service rate. From Fig. 2 we see that 0 to 𝑛 states represent any arrival job (i.e. new call, handover or permanent user) and from 𝑛 to 𝑎 states are reserved for permanent user allocation only. So if 𝑃𝑐 represents the permanent user channels and 𝑎 states represent total number of channels then the remaining number of channels for handovers and new calls is given by: 𝑛 = 𝑎 − (𝑃𝑐) (1) Using the Fig. 2 and the basic equation work performed in [4] and [5] let us consider that 𝑃𝑗 is the statistical probability for total 𝑗 states, then for 0 ≤ 𝑗 < 𝑛 the transition rate for 𝑃𝑗 to 𝑃𝑗+1 states is given by 𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 and for 𝑃𝑗+1 to 𝑃𝑗 is given by (𝑗 + 1)(µ𝑜 + µℎ + µ𝑝 ). From 𝑛 ≤ 𝑗 < 𝑎 states the transition rate for 𝑃𝑗 to 𝑃𝑗+1 is given by 𝜆𝑝 because handovers and new calls are not allowed to occupy these channels only high priority users have access to these channels. The transition rate from 𝑃𝑗+1 to 𝑃𝑗 for 𝑛 ≤ 𝑗 < 𝑎 is given by(𝑗 + 1)(µ𝑜 + µℎ + µ𝑝 ). We calculate the blocking probabilities as follows: 𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 𝑗 ( ) µ𝑜 + µℎ + µ𝑝 𝑃𝑗 = 𝑃𝑜 𝑓𝑜𝑟 0 < 𝑗 ≤ 𝑛 (2) 𝑗! 𝑛 (𝜆𝑃 )𝑗−𝑛 (𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 ) 𝑃𝑗 = 𝑃𝑜 𝑓𝑜𝑟 𝑛 < 𝑗 ≤ 𝑎 (3) 𝑗 𝑗! (µ𝑜 + µℎ + µ𝑝 ) Using (2) and (3) we provide the probabilities of total 𝑎 states. Let us consider:

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Figure 3. Markov Chain model for RAHPA.

𝑗

𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 ) µ𝑜 + µℎ + µ𝑝 = 𝑥𝑗 𝑗! 𝑛 (𝜆𝑃 )𝑗−𝑛 (𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 ) = 𝑦𝑗 𝑗 𝑗! (µ𝑜 + µℎ + µ𝑝 ) (

(4) (5)

So (2) and (3) become: 𝑃𝑗 = 𝑥𝑗 𝑃𝑜 𝑃𝑗 = 𝑦𝑗 𝑃𝑜

𝑓𝑜𝑟 0 < 𝑗 ≤ 𝑛 𝑓𝑜𝑟 0 < 𝑗 ≤ 𝑛

(6) (7)

As this is a 2-dimensional Markov model and to find 𝑃𝑗 we need to find the probability of the zero-state denoted by 𝑃0 . To find 𝑃0 we use the total probability equation: 𝑎

∑ 𝑃𝑗 = 1

(8)

𝑗=0

Solving (6), (7) and (8) we get: 𝑃𝑜 =

∑𝑛𝑗=0 𝑥𝑗

1 + ∑𝑎𝑗=𝑛+1 𝑦𝑗

(9)

The blocking probability for new calls is dependent on number of unavailable channels i.e. from 𝑛 to 𝑎 states, so: 𝑎

𝑃𝑏 = ∑ 𝑃𝑗

(10)

𝑗=𝑛

As handovers have the same priority compared to new calls, so handover failure blocking probability is given by: 𝑃ℎ = 𝑃𝑏

(11)

Permanent user channel blocking probability is given by: 𝑃𝑝 = 𝑃𝑎

(12)

Where 𝑃𝑎 is calculated by solving (6), (7), (9) and replacing 𝐽 by 𝑎: 𝑃𝑎 = (𝑥𝑎 + 𝑦𝑎 )𝑃𝑜 (13) 2.2 Reserved Allocation for Handovers and Permanent Assignment The model presented in Fig. 3 is also based on a 2dimensional Markov Chain process. In this model, we have reserved channels for handovers and permanent user allocation. The remaining channels are for new calls but still the high priority users (i.e. handover and permanent) can be allocated remaining channels upon unavailability of reserved ones. In Fig. 3 we have total 𝑎 states where, 𝜆𝑜 is the new call arrival rate, 𝜆ℎ is the handover arrival rate, 𝜆𝑝 is the permanent job arrival rate, µℎ is the handover service rate, µ𝑂 is new call service rate and µ𝑃 is permanent job service rate. From Fig. 3 we see that 0 to 𝑛 states represent any arrival job (i.e. new call, handover or permanent user), from 𝑛 to s states are reserved for handover and permanent allocation and from s to 𝑎 states only permanent user allocation. One important thing to remember is that whenever a high priority job arrives, it will be allocated channel from its reserved space, but if no channel is available only then it can utilize the remaining channels. So, if 𝑃𝑐 represents the permanent channels, ℎ represents the handover channels and 𝑎 states represent the total channels then the remaining number of channels for new calls is given by: 𝑛 = 𝑎 − (ℎ + 𝑃𝑐) (14) To find the total state probability, from Fig. 3 let us consider that 𝑃𝑗 is the statistical probability for total 𝑗 states, then for 0 ≤ 𝑗 < 𝑛 the transition rate for 𝑃𝑗 to 𝑃𝑗+1 states is given by 𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 and for 𝑃𝑗+1 to 𝑃𝑗 is given by (𝑗 + 1)(µ𝑜 + µℎ + µ𝑝 ). From 𝑛 ≤ 𝑗 < 𝑠 states the transition rate for 𝑃𝑗 to 𝑃𝑗+1 is given by 𝜆ℎ + 𝜆𝑝 and the transition rate from 𝑃𝑗+1 to 𝑃𝑗 is given by (𝑗 + 1)(µ𝑜 + µℎ + µ𝑝 ) because new calls are not allowed to occupy these channels, only handover and high priority users have access to these channels. From s ≤ 𝑗 < 𝑎 states, the transition rate for 𝑃𝑗 to 𝑃𝑗+1 is given by 𝜆𝑝 and the transition rate from 𝑃𝑗+1 to 𝑃𝑗 is given by (𝑗 + 1)(µ𝑜 + µℎ + µ𝑝 )because both handovers and new calls are

Template for submitting papers to IETE Journal of Research. denied access to these channels except the permanent users. We provide the state probabilities as follows: 𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 𝑗 ( ) µ𝑜 + µℎ + µ𝑝 𝑃𝑗 = 𝑃𝑜 𝑓𝑜𝑟 0 < 𝑗 ≤ 𝑛 (15) 𝑗! 𝑛 (𝜆𝑃 +𝜆ℎ )𝑗−𝑛 (𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 ) 𝑃𝑗 = 𝑃𝑜 𝑓𝑜𝑟 𝑛 < 𝑗 ≤ 𝑠 (16) 𝑗 𝑗! (µ𝑜 + µℎ + µ𝑝 ) 𝑛 (𝜆𝑃 )𝑗−(𝑠+𝑛) (𝜆𝑃+ 𝜆ℎ )𝑠−𝑛 (𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 ) 𝑃𝑗 = 𝑃𝑜 𝑗 𝑗! (µ𝑜 + µℎ + µ𝑝 ) 𝑓𝑜𝑟 𝑠 < 𝑗 ≤ 𝑎 (17) Let us consider: 𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 𝑗 ) µ𝑜 + µℎ + µ𝑝 = 𝑢𝑗 𝑗! 𝑛 (𝜆𝑃+ 𝜆ℎ )𝑗−𝑛 (𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 )

4 In [4], it is shown that the handover arrival rate from all the sides of a hexagon cell is given by: 6

𝜆ℎ (𝑘) = 𝑞(𝑘, 𝑖) ∑ 𝜆ℎ𝑜 (𝑖)

(29)

i=1

For both proposed models in Fig. 2 and Fig. 3, the probability that a mobile user leaves the hexagon cell from each side is equal, i.e., 𝑞(𝑘, 𝑖) = 1/6. Where 𝑘 is the call initiation cell, 𝑖 is the target cell and 𝜆ℎ𝑜 is the handover departure rate towards the target cell. The traffic conditions are considered to be uniform, so 𝜆ℎ (𝑘) = 𝜆ℎ𝑜 (𝑘) or simply 𝜆ℎ = 𝜆ℎ𝑜 . To calculate the probabilities, 𝑃𝑏 , 𝑃ℎ and 𝑃𝑝 , the proposed algorithm is as follows:

(

= 𝑣𝑗 𝑗 𝑗! (µ𝑜 + µℎ + µ𝑝 ) 𝑛 (𝜆𝑃 )𝑗−(𝑠+𝑛) (𝜆𝑃+ 𝜆ℎ )𝑠−𝑛 (𝜆𝑜 + 𝜆ℎ + 𝜆𝑝 ) 𝑗! (µ𝑜 + µℎ + µ𝑝 )

𝑗

(18) (19) = 𝑤𝑗

(20) 𝜆ℎ𝑜

So (13), (14) and (15) can be presented as: 𝑃𝑗 = 𝑢𝑗 𝑃𝑜 𝑃𝑗 = 𝑣𝑗 𝑃𝑜 𝑃𝑗 = 𝑤𝑗 𝑃𝑜

𝑓𝑜𝑟 0 < 𝑗 ≤ 𝑛 𝑓𝑜𝑟 𝑛 < 𝑗 ≤ 𝑠 𝑓𝑜𝑟 𝑠 < 𝑗 ≤ 𝑎

Step A: Input: 1. Total number of channels (a states) 2. Percentage of handover channels (only for RAPA) 3. Percentage of permanent channels Step B: Calculate 𝜆𝑜 , 𝜆ℎ and 𝜆𝑝 :

(21) (22) (23)

To find the zero-state probability 𝑃0 we solve (8), (21), (22) and (23) resulting in: 1 𝑃𝑜 = 𝑛 (24) ∑𝑗=0 𝑢𝑗 + ∑𝑠𝑗=𝑛+1 𝑣𝑗 + ∑𝑎𝑗=𝑠+1 𝑤𝑗 In this model also, the blocking probability for a new call is dependent on number of unavailable channels i.e. from 𝑛 to 𝑎 states, so:

𝜆𝑜 = 𝜌 ∗ µ𝑜 𝜆𝑝 = 𝜌 ∗ µ𝑝 = (𝑃𝑝,𝑠𝑢𝑐𝑐𝑒𝑠𝑠 ∗ 𝜆𝑝 ) + (𝑃𝑏,𝑠𝑢𝑐𝑐𝑒𝑠𝑠 ∗ 𝜆𝑜 )

(30) (31) (32)

Where, 𝜌 is the offered traffic and is equal to the total number channels and (32) is modified from [4]. In (31) 𝑃𝑝,𝑠𝑢𝑐𝑐𝑒𝑠𝑠 is the probability of success for permanent user calls and 𝑃𝑏,𝑠𝑢𝑐𝑐𝑒𝑠𝑠 is the probability of success for the new calls and are given by: 𝑃𝑝,𝑠𝑢𝑐𝑐𝑒𝑠𝑠 = 1 − 𝑃𝑝 (33) 𝑃𝑏,𝑠𝑢𝑐𝑐𝑒𝑠𝑠 = 1 − 𝑃𝑏 (34) Step C: Calculate 𝑃𝑏 , 𝑃ℎ and 𝑃𝑝 according to the proposed models in the subsections A and B of this section. After the probability calculations to perform the risk analysis Palisade @ Risk is used.

𝑎

𝑃𝑏 = ∑ 𝑃𝑗

(25)

𝑗=𝑛

The channels from 𝑠 + 1 to 𝑎 will be unavailable for handovers so we provide the handover failure probability by: 𝑎

𝑃ℎ = ∑ 𝑃𝑗

(26)

𝑗=𝑠+1

and the permanent user blocking probability by: 𝑃𝑝 = 𝑃𝑎

(27)

Where we calculate 𝑃𝑎 by solving (21), (22), (23), (24) and replacing 𝐽 by 𝑎: 𝑃𝑎 = (𝑣𝑎 + 𝑢𝑎 + 𝑤𝑎 )𝑃𝑜 (28)

2.3 Palisade @ Risk: Risk Analysis In this subsection, we explain that what is Palisade @ Risk and how we used it to our benefit. @Risk, also pronounced as at risk, is mostly used in the field of project management for risk reduction by predicting future values. It uses Monte Carlo simulation to show the possible outcomes and also let us know that how likely they would occur. From simulation results we can analyze the risks associated with the outcomes and then decisions can be made to avoid the uncertain situations [14]. Monte Carlo simulation uses different probability distributions, according to the available data, in order to predict the outcomes [15]. In our case, we have used binomial distribution which requires the probability of success or failure (𝑃𝑆𝑢𝑐𝑐𝑒𝑠𝑠 or 𝑃𝐹𝑎𝑖𝑙𝑢𝑟𝑒 ) and the number of trials N, as inputs, to predict the outcomes [16]. From the outcomes, we can find out the most likely scenario to occur. So, in this paper we have considered the number of trials as the number of channels and probability values will be taken from the MATLAB results for

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respective channels. We have provided the outcomes and their descriptions in the simulation section.

SIMULATION RESULTS

This section is divided in two parts, i.e., the blocking probability evaluation and risk analysis. 3.1 Blocking Probability To simulate the models proposed in the Section II, we have considered a single hexagon cell with six neighbors, one at each side, and uniform traffic conditions. User mobility is considered as a two-dimensional walk with probability that a user leaves the hexagon from each side is 1/6. The time for which the user remains in the cell before moving to a neighbor is given by 1/µℎ and the times for which new call and permanent user call will be connected to the system are given by 1/µ𝑜 and 1/µ𝑃 respectively. The arrival rates 𝜆𝑜 , 𝜆ℎ and 𝜆𝑝 are determined using µ𝑂 , µ𝑃 and µℎ . The number of channels allocated to a cell range from 60 to 100. The percentage of permanent user channels is set to 5% and for handover channels is set to 10%. The simulation results for the blocking probabilities under consideration, i.e., 𝑃𝑏 , 𝑃ℎ and 𝑃𝑝 , are shown in Figs. 4-6. Fig. 4 shows the results for 𝑃𝑏 , 𝑃ℎ and 𝑃𝑝 using the RAPA model. It can be seen that, by reserving the number of channels for permanent users, the blocking is significantly reduced, almost negligible. The blocking probability for handovers and newly initialed calls is higher because there are no reserved channels for these jobs. One more thing can be noticed is that handover blocking probability and new call blocking probability overlap each other, because their probability of occurrence is same. Fig. 5 shows the results for 𝑃𝑏 , 𝑃ℎ and 𝑃𝑝 using the RAHPA model. It can be observed that the probability of permanent user blocking is reduced significantly, almost negligible. The blocking probability of handovers is also reduced to a significant level because in RAHPA we also have reserved

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Figure 5. Blocking probability curves for RAHPA against the number of channels. The percentage of handover channels is 10% and the percentage of permanent user channels is 5%. Mean service times, 𝟏/µ𝑶 , 𝟏/µ𝑷 and 𝟏/µ𝒉 are set to 3 min.

channels for performing handover. The only tradeoff is that the new calls blocking probability is increased as there are less number of channels available for this job. But this tradeoff is acceptable as from the QoS point of view, ongoing call termination is considered worse than the newly initiated call being blocked. The comparison of both proposed models can be seen in Fig. 6. We can see that the new call blocking probability is higher in RAHPA than RAPA because the channels available for new calls are less in RAHPA than RAPA. But at the same end, the handover blocking probability is reduced in RAHPA. So, as explained for Fig. 5 earlier, this is a tradeoff and from QoS point of view this tradeoff is acceptable, as handover failure results in ongoing call’s forceful termination. The permanent user blocking probability is same in both models as the reserved channels, considered for both RAPA and RAHPA, are same, i.e., 5%. 0

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Figure 4. Blocking probability curves for RAPA against the number of channels. The percentage of permanent user channels is 5% and the mean service times, 𝟏/µ𝑶 , 𝟏/µ𝑷 and 𝟏/µ𝒉 are set to 3 min.

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Figure 6. Comparison between the blocking probability curves of RAPA and RAHPA. The percentage of handover channels is 10% and the percentage of permanent user channels is 5%. Mean service times 𝟏/µ𝑶 , 𝟏/µ𝑷 and 𝟏/µ𝒉 are set to 3 min.

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Figure 7. @Risk binomial distribution histogram for new call blocking using RAHPA. No. of channels = 70 and the corresponding new call blocking probability Pb = 0.0505. Shaded region provides total blocking area.

3.2 Risk Analysis This part will provide the explanation and discussion of risk analysis using the @ Risk simulation results. As explained in the Subsection C of Section II that @ Risk uses Monte Carlo simulations to predict the outcome, so it is important to choose a distribution that suits to our scenario for best prediction. In our case, we have used binomial distribution to perform the simulations. We chose binomial distribution because it requires number of trials and their probability of success or failure as an input to provide the output PDF. When binomial distribution is used in @ Risk, it will make use of the Monte Carlo simulations to provide an output histogram with the best possible predictions, i.e., the range of successful or failed trials (horizontal axis) with their respective frequencies of occurrence (vertical axis). In our case the number of trials is considered as the number of channels and the probability is considered as the probability of failure, i.e., probability that a new user will be blocked. For simulating the results in Figs. 7-9 we have considered 70 total channels with their corresponding new call blocking probability for RAHPA, i.e., 𝑃𝑏 = 0.0505. The probability value is taken from the MATLAB results shown in Fig. 5. In the simulation results, shown in Figs. 7-11, the vertical boundary lines of the shaded region can be moved (in the @ Risk simulation tool) to check the percentage of blocking for a specific range within the total blocking area. By moving the shaded area, the region where minimum and maximum blocking occurs can also be found. According to the input data (70 channels with 𝑃𝑏 = 0.0505) Fig. 7 shows that the total area of blocking most likely lies between channels 0 and 9. The shaded region tells us that there are 98% chances that blocking will occur within this area. Figs. 8 and 9 are extended from Fig. 7 for the interpretation of maximum and minimum percentage of blocking occurrence respectively. The shaded region in Fig. 8 shows that channels 2 and 3 have the maximum percentage of blocking occurrence,

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Figure 8. @Risk binomial distribution histogram for new call blocking using RAHPA. No. of channels = 70 and the corresponding new call blocking probability Pb = 0.0505. Shaded region provides blocking for channel 2 and channel 3.

i.e., 23% and the shaded region in Fig. 9 shows that channels 8 and 9 have the minimum percentage of blocking occurrence, i.e., 1%. The shaded region can be moved (in @Risk simulation tool) to check the blocking probability occurrence for other channels as well. By varying the blocking probability values (independent of RAHPA or RAPA) it was also observed that, if the value of 𝑃𝑏 lies between 0 to 0.5, then the channels blocked will most likely lie in the range below the median value, and if 𝑃𝑏 is above 0.5 then above the median value. In our simulation case, we have 70 channels so median is 35. This can be observed in Figs. 10-11. In Fig. 10 the value of 𝑃𝑏 is below 0.5 and in Fig. 11 it is above 0.5.

4.

CONCLUSION

In this work two models, RAPA and RAHPA for high priority user channel assignment, in wireless cellular network are

Figure 9. @Risk binomial distribution histogram for new call blocking using RAHPA. No. of channels = 70 and the corresponding new call blocking probability Pb = 0.0505. Shaded region provides blocking for channel 8 and channel 9.

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Figure 10. @Risk binomial distribution histogram for new call blocking. No. of channels = 70 with Pb = 0.2. Most likely region where blocking can occur is between 5 to 24 channels.

proposed. The call blocking and handover failure probabilities for newly initiated calls and high priority users (e.g. Military, Police and emergency services etc.) have been derived for both RAPA and RAHPA. In both models, reserving permanent user channels has shown a significant reduction in the blocking probability of high priority users (almost negligible). In RAHPA, reserving the channels for handovers has also shown a significant reduction in the handover failure probability. Handover failure reduction is important for high priority mobile users as it will reduce the forceful termination of calls. Only tradeoff, using RAPA and RAHPA, is the increase in blocking probability of newly originated calls. As high priority users blocking and handover failure results in bad QoS, so this tradeoff is acceptable in terms of the QoS of the system. Secondly, it can be seen that the blocking probability of newly originated calls is not so high if we keep the percentage of the reserved channels limited according to the traffic conditions. To achieve even better results, these models can also be implemented using DCA or HCA; however, this is beyond the scope of this paper. The risk analysis provides detail information on the future prediction that which channels will be busy out of the total number of channels used. Secondly, we can also check the blocking probability occurrence of individual channels as well. Here one important thing to remember is that use of risk analysis requires efficient historical data, so the input blocking probabilities should be based on the efficient collection of the past blocking events. However, in this paper only the use of @Risk for prediction of blocked channels and their probability of occurrence is provided but this can be tested in real time for the validation purpose. Secondly the validity of Models proposed can also be tested in real time or by creating a test bed.

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Figure 11. @Risk binomial distribution histogram for new call blocking. No. of channels = 70 with Pb = 0.7. Most likely region where blocking can occur is between 40 to 59 channels.

REFERENCES 1. Siemens Networks, White Paper “2020: Beyond 4G Radio Evolution for the Gigabit Experience”. Available: http://networks.nokia.com/system/files/document/n okia_siemens_networks_beyond_4g_white_paper_onlin e_20082011_0.pdf. 2. Fricke, Matthias, Andrea Heckwolf, Ralf Herber, Ralf Nitsch, Silvia Schwarze, and Stefan Voß. "Requirements of 4G-Based Mobile Broadband on Future Transport Networks", Journal of Telecommunications and Information Technology, Vol.2, pp: 21-28, 2012 3. Sidi, Moshe, and David Starobinski. "New call blocking versus handoff blocking in cellular networks", Wireless networks, Vol. 3, no.1, pp: 15-27, March 1997 4. L. O. Guerrero, A. H. Aghvami. "A prioritized handoff dynamic channel allocation strategy for PCS", Vehicular Technology, IEEE Transactions on, Vol. 48, no. 4, pp: 1203-1215, Jul 1999. 5. A. A. Siddiqui, M. Y. I. Zia. "New calls blocking analysis in cellular systems based on Markov chain model." In Networking and Communication, INCC, International IEEE Conference, pp: 69-72, June 2004. 6. Lin, Yi-Bing, Seshadri Mohan, and Anthony Noerpel. "Queueing priority channel assignment strategies for PCS hand-off and initial access." Vehicular Technology, IEEE Transactions on, Vol. 43, no. 3, pp: 704-712, Aug 1994. 7. Tekinay, Sirin, and Bijan Jabbari, "A measurementbased prioritization scheme for handovers in mobile cellular networks", Selected Areas in Communications, IEEE Journal on, Vol. 10, no. 8, pp.: 1343-1350, Oct 1992. 8. Du, Wenfeng, Weijia Jia, Guojun Wang, and Wenyan Lu, "Analysis of channel allocation scheme for wireless cellular networks", International Journal of Ad Hoc and Ubiquitous Computing, Vol. 4, no. 3, pp.: 201-209, 2009

Template for submitting papers to IETE Journal of Research. 9. M. Zhang, P. Yum Tak-Shing "Comparisons of channelassignment strategies in cellular mobile telephone systems", Vehicular Technology, IEEE Transactions on, Vol. 38, no. 4, pp.: 211-215, Nov 1989 10. Xuming Fang, Changqian Zhu, Pingzhi Fan, "Compact pattern based channel borrowing assignment strategy in cellular mobile systems", In Vehicular Technology Conference, IEEE 49th, vol. 1, pp. 6-9, May 1999. 11. Chuan-jiang Yan, Fang-ming Zhao, Wei Wang and Di He, “A pre-emptive channel borrowing scheme and performance analysis for wireless overlay networks", Neural Networks and Signal Processing, 2008 International Conference on, IEEE, pp. 598-603, June 2008. 12. Muhammad Rehan Usman, Johar Iqbal and Fahad Razzaq, "Performance Analysis of Channel Allocation Schemes In Wimax", University Essay From Blekinge Tekniska Högskola, 2009. Available: http://seamist.se/fou/cuppsats.nsf/all/191feefadaa24104c1257 682004a0bb1/$file/masterfinalthesis.pdf. 13. C. M. Grinstead, and J. L. Snell, “Introduction to probability”, Chapter 11, American Mathematical Soc., 1998. 14. Palisade, “The future in your spreadsheet”, Available: http://www.palisade.com/risk/ 15. Palisade, “Monte Carlo simulation”, Available: http://www.palisade.com/risk/monte_carlo_simulatio n.asp 16. Rubinstein, Reuven Y., and Dirk P. Kroese, Chapter 1, “Preliminaries”, Vol. 707. John Wiley & Sons, 2011.

M. Rehan Usman was born in Lahore City, Pakistan in 1986. He received the B.S. degree in Electrical Engineering from COMSATS Institute of Information Technology Lahore, Pakistan, in 2008 and holds two M.S. Degrees, i.e., 1) M.S. Electrical Engineering with Specialization in Telecommunications from BTH, Sweden, in 2010 and 2) M.S. in Project Management and Operational Development from KTH, Sweden, in 2013. He was a Lecturer in Electrical Engineering department at University of South Asia Pakistan from July 2012 to January 2013. Then he joined as a Lecturer in Electrical Engineering department of Superior University Lahore, Pakistan, from January 2013 to March 2014. After serving in Superior University he is now a PhD research scholar at WENS Lab in School of Electronics in Kumoh National Institute of Technology since March 2014. His research interests include coexistence among networks,

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cognitive radio, MIMO, OFDM, NOMA, small cells and next generation mobile wireless networks (4G/5G). Soo Young Shin was born in 1975. He received his B.S., M.S., and Ph. D degrees in Electrical Engineering and Computer Science from Seoul National University, Korea in 1999, 2001, and 2006, respectively. He was a visiting scholar in FUNLab at University of Washington, US, from July 2006 to June 2007. After 3 years working in WiMAX design lab. of Samsung Electronics, he is now assistant professor in School of Electronics in Kumoh National Institute of Technology since September 2010. His research interests include wireless LAN, WPAN, WBAN, wireless mesh network, sensor networks, coexistence among wireless networks, industrial and military network, cognitive radio networks, MIMO, OFDM, mmWave, NOMA and next generation mobile wireless broadband networks (4G/5G).