On the Design of Delay based Admission Control in Hierarchical Networks

Abstract

Today, as the hierarchical cellular system is getting more attention than before, some recent studies introduce delay based admission control (AC) scheme which delays the admission to the macro-embedded small cell for a relatively short time to prevent unnecessary handover caused by the short-term visitors of the small cell area. In such delay based ACs, when we use improper delay parameter, the system frequently makes incorrect handover decisions such as where unnecessary handover is allowed due to too short delaying, or where necessary handover is denied due to too long delaying. In order to avoid these undesirable situations as much as possible, we develop a new delay parameter decision method based on probabilistic cell residence time approximations. By the extensive numerical and analytical evaluations, we determine the proper delay parameter which prevents the incorrect handover decision as much as possible. We expect our delay parameter decision method can be useful system administration tips in hierarchical cellular system where delay based AC is adopted.

1. Introduction

Hierarchical cellular network is a type of cellular network where a macro cell includes many macro-embedded small cells such as mirco, femto cells or Wi-Fi hotspots [1][2][3]. Exploiting the low deployment and administration costs of small cells, the hierarchical cellular network provides enhanced spatial capacity compared to conventional macro cell only system with relatively low costs. However, in hierarchical network, as the number of macro-embedded small cell increases, the macro base stations has to bear large burdens to process so many inter-tier handovers as illustrated in Fig. 1. Hence, reducing unnecessary handover is one of the important matters in hierarchical multi-tier systems [4][5].

Fig. 1.Frequent inter-tier handovers in hierarchical cellular networks

Conventionally, the term unnecessary handover refers to ping-pong effect which means that the mobile station continues to be handed back and forth between two base stations at cell boundary area [6]. In hierarchical cellular network, however, it is desirable to make the term unnecessary handover have broader definition. According to the measurement from the wireless test-bed in Carnegie Mellon University [7], around 50% and 70% of mobile users stay in small cells1 for less than 3 and 10 seconds respectively. From this, unnecessary handover need to include not only the ping-pong effect, but also the handovers caused by short-term residence users who stay in a small cell for less than given time discriminant decided by network administrator. Thereby, if we prevent such a short-term residence user from being handed to the small cell, the number of unnecessary handover will be significantly reduced.

To filter out the handover of short-term residence user, recent studies introduce delay based admission control (AC) for macro → small cell handover decision [8][9][10][11][12]. In the delay based AC, when the user comes into the small cell area, the system does not start the handover process immediately. Rather, the system suspends the handover until pre-determined delay time goes by. If the user is still within the small area after delay time, the system eventually starts handover process. Conversely, if the mobile user comes back out of the small cell before the delay time elapses, the macro → small cell handover is automatically avoided. By this mechanism, delay based AC suppresses the occurrence of unnecessary handovers made by short-term residence users. The delay based AC is simple, but efficient enough to prevent unnecessary handovers of short-term visitors like who quickly passes by the edge of the small cell area.

However, there are still an important problematic issue about delay parameter decisions. If we use too short delay parameter, the protocol may improperly allow unnecessary handovers made by short-term residence users. On the other hands, if we use too long delay parameter, the system prevent not only unnecessary handover, but also unnecessary handover made by long-term enough residence user. Hence, we need to choose the delay parameter such that the possibility of above incorrect decision is minimized.

By observing the cases of incorrect handover decisions in delay based AC, we discover that the occurrence of incorrect handover decision can be checked by the relationships among the user’s cell residence time tR, short-residence time discriminant tTh, and the delay parameter d. Based on the observations, we make a new performance metric called as incorrect handover decision probability which quantifies the possibility of incorrect handover decision. From this, we can represent the proper delay parameter decision problem as the optimization problem which chooses the delay parameter d that minimizes the incorrect handover decision probability.

By using extensive numerical evaluations, we observe how of tR, tTh, and d affect the incorrect handover decision probability. From the numerical results, we determine the proper delay parameter. Our delay parameter decision method make the delay based AC significantly reduce the number of macro → small cell handover with relatively low incorrect handover decision probability.

To the best of our knowledge, our work is first research about the delay parameter decision steps in delay based AC. Existing works consider only the handover decision or processing steps assuming the proper delay parameter is already given [8][9][10][11][12]. We expect our work is useful reference to the network administrator who operates hierarchical cellular network where delay based AC is adopted for macro → small cell handover.

The remaining part of this paper is as followings: In section 2, we explain delay based AC from the protocol perspective. Delay parameter design problem is discussed in section 3. Then, numerical evaluations are presented in section 4. Finally, we conclude in section 5.

 

2. Delay based Admission Control

As described in section 1, delay based AC refers to delaying macro → small cell handover for pre-determined delay time when the mobile user comes into the small cell area. Actually, whether the mobile user is within the small cell area is determined by checking SINR (Signal-to-Interference-and-Noise-Ratio) of the small cell base station. Thus, delay based AC is implemented by modifying the SINR scanning and handover decision procedure of conventional AC protocol. Detailed procedures are as followings:

Step 1: If the mobile device is approaching to the base station of small cell S, it detects the signals of S by periodical signal scanning. (The scanning interval is varied from few tens of milliseconds to few tens of seconds [13].) Here, the system checks if the following condition is satisfied:

where SM is the SINR of currently connected macro cell, SS is the SINR of the target small cell, α(0≤α≤1) is scaling factor, Δ and is the hysteresis to prevent ping-pong effect. Eq. (2.1) is the SINR condition for macro → small cell handover proposed by Moon et. al [14]. Of course, it is no matter to use another type of criterion according to administration policy. For example, we can change eq. (2.1) to the handover criterions proposed by [15] [16] [17] which are designed to enhance the various system performance.

Step 2: When eq. (2.1) is satisfied, the system assumes that the mobile user comes into the small cell area. However, the system does not start macro → small cell handover immediately. Instead, the system makes the reservation for the handover after waiting for d. It generates the timestamp tS which is used for checking the cell residence time of the mobile user.

Step 3: After the reservation, whenever the scanning period returns, the system checks if eq. (2.1) is still satisfied. If it is, the system proceeds to step 5 as next procedure. Otherwise, the system proceeds to step 4.

Step 4: Step 4: In this case, the system assumes that the mobile user comes back out of the small cell. And then, it destroys tS to cancel the reservation for macro → small cell handover. By this mechanism, unnecessary handover of short-term residence user is automatically avoided.

Step 5: In this case, the system assumes that the mobile user still stays in the small cell area. Then, it calculates the difference of the present time tP and timestamp tS. If the difference is smaller than d, the system turns back to step 3. Otherwise, the system eventually starts macro → small cell handover. At this moment, |tP - tS| ≥ d means that the delay time elapses.

 

3. Delay Parameter Design Problem

3.1 Decision Correctness of Delay based AC

The goal of delay based AC is preventing unnecessary handovers made by short-term residence users. However, as discussed earlier, improper delay parameter may cause the delay based AC makes incorrect handover decision such as denying of necessary handover, or allowance of unnecessary handover. To formulate the decision correctness of delay based AC, we define a decision verifier function v(tR, tTh, d) as following:

In the eq. (3.1), case 1 means the proper allowance of necessary handover as illustrated in Fig. 2 (a). Here, one notable thing is that we use tR-d≥tTh instead of tR≥tTh as a criterion of proper handover allowance. This is because, in delay based AC, the effective access time to the small cell is tR-d due to delaying before the actual macro → small cell handover. And, case 2 means the proper prevention of unnecessary handover as illustrated in Fig. 2 (b). Case 3 means all improper situations which do not satisfy the conditions of case 1 or 2.

Fig. 2.The examples of correct decision of delay based AC

3.2 Determining the Proper Delay Parameter

Considering the goal of the delay based AC, eq. (3.1) is an essential component to determine the proper delay parameter d. In other words, it is desirable to determine d such that the system avoids the situation where v(tR, tTh, d)=0 as much as possible. For easier understanding, let us look at an example where a system uses delay based AC and tTh is 3 seconds. If a mobile user comes and stays in the small cell for 7 seconds, we need to set d≤4 to make v(7,3,d)=1.

If the system knows exactly in advance tR of the incoming mobile user to the small cells, we will always makes v(tR, tTh, d)=1 However, unfortunately, it is impossible because the cell residence time of each user which is undeterministic. Therefore, the most practical approach is to set d as a constant that minimizes the probability of v(tR, tTh, d)=0 for given tTh and tR. Since tR is undeterministic, it can be expressed as a random variable. Hence, determining the proper delay parameter of delay based AC can be following minimization problem:

where tTh is given by network administrator, and tR is a random variable which follows an arbitrary probability distribution. The probability distribution function of tR can be obtained by approximating the statistics about the user residence time collected by base stations. And from now on, we refer Pr[v(tR, tTh, d)=0] to incorrect handover decision probability.

The next thing we have to do is to discover how we calculate incorrect handover decision probability. According to our observation, whether v(tR, tTh, d)=0 or not is determined by the relationships among tR, tTh, and d. There are 8 distinct size relationships made from (tR, tTh, d)-tuples. For each case, we study when v(tR, tTh, d)=0. We list the situational analysis for each case as followings which is previously introduced by [21]:

Case 1 (tR

Case 2 (dd. However, since tR

Case 3 (d≤tTh≤tR

Case 4 (d≤tThd+tTh(⇔tR-d>tTh). In this case, the delay based AC properly allows necessary handover made by enough-residence time user.

Case 5 (tR

Case 6 (tTh≤tRtTh. This case means that the necessary handover is incorrectly suppressed due to delay based AC.

Case 7 (tTh

Case 8 (tThd. And, v(tR, tTh, d)=1, due to tR≥d+tTh(⇔tR-d≥tTh). In this case, necessary handover is properly admitted.

Among above 8 cases, when the delay based AC makes incorrect decision are the case 2, 3, 6, and 7. When we have the probability distribution of tR, we can obtain the incorrect handover decision probability by summing the probabilities of these cases. Hence, the incorrect handover decision probability is as

It is obvious that the incorrect handover decision probability is directly derived by the pdf (probability density function) or cdf (cumulative distribution function) of tR. Thus, when tTh is given from network administrator, the minimization problem (3.2) is solved by using the pdf or cdf of tR.

By observing the eq. (3.2) and (3.3), we find a useful property: the solution of (3.2) cannot be higher than tTh. Thus, we do not have to consider the case d>tTh any more when we determine the proper delay parameter. Now, eq. (3.2) can be modified as

Eq. (3.4) can be solved by the numerical minimization technique when the constant tTh and the random variable tR are given [17]. Even if is complicated form and so difficult to apply well-known minimization technique, we can obtain practical approximate solution by exhaustive searching with limited accuracy of d such as few milliseconds. With this equation, we conduct numerical evaluations of our delaying handover scheme in the next section.

 

4. Numerical Evaluations

In this section, we perform numerical experiments to look at the effects of tTh and d on the incorrect handover decision probability. Khan et. al study various probability distribution functions which can be used to describe the cell residence time of mobile users [18]. By using those functions as the pdf of tR, we measure how incorrect handover decision probability and handover reduction ratio changes with respect to tThand d. The handover reduction ratio Rh is the ratio of users whose residence time is less than d to the total mobile users. This can be expressed as

The table 1 lists the types and their pdfs which specify tR in our experiments. Among the distributions in [7], we omit Erlang and Uniform distributions in our experiments. This is because (a) we already use Gamma distribution which is the generalization of Erlang distribution and (b) Uniform distribution is not realistic [19].

Table 1.The probability distributions used for experiments

To make tR have short-term residence property, we decide the parameters of each distribution in the table 1 such that (a) median is 3 seconds, and (b) 50 ~ 55% of the random variable is less than median. These characteristics are based on the measurement data in [7] which studies the cell residence time of mobile users in small-scale cellular networks. The input distributions of tR in our experiments are as followings:

Using the equations (4.2) - (4.5) as inputs, we measure the incorrect handover decision probabilities and handover reduction ratios.

Fig. 3 shows the numerical results of Exponential distribution for eq. (4.2). Fig. 3 (a) shows how the incorrect handover decision probability changes according to tTh and d. In this figure, we can see that the incorrect handover decision probability is smaller when tTh = d than when tTh ≠ d. In short, the optimal delay parameter is tTh. In fact, this property holds when the pdf of tR is monotonic decreasing function. We present generalized theorem about it later. Fig. 3 (b) shows the incorrect handover decision probability according to tTh where d is the solution of eq. (3.6). Since the optimal solution of (3.6) is equivalent to tTh in this case, the figure shows the values of The plot increases until at around 2.6 seconds, and then decreases thereafter. The highest incorrect handover decision probability is around 25% when tTh is at around 2.6 seconds. Fig. 3 (c) plots the handover reduction rate according to tTh. Same as the Fig. 3 (b), this result is also about where d=tTh. As tTh increases, the amount of handover avoidance also increases. Due to Rh=Pr[tR

Fig. 3.The numerical results for tR~Exp(0.2634): (a) incorrect handover decision probability according to tTh and d (b) incorrect handover decision probability according to tTh (c) handover reduction probability according to tTh

Fig. 4 shows the numerical results of the Gamma distribution for eq. (4.3). Fig. 4 (a) shows how the incorrect handover decision probability changes according to tTh and d. In the figure, we can see that the proper delay parameter is different upon the value of tTh. When tTh is within the range where the pdf of tR increases, the incorrect handover decision probability is decreased as d decreases. Namely, the incorrect handover decision probability is minimized when d=0. On the other hands, when tTh is within the range where the pdf of tR decreases, the solution of the equation (3.6) is tTh. This is same as in the case of Exponential distributions. Fig. 4 (b) shows incorrect handover decision probability according to tTh where d is the solution of eq. (3.6). Thus, in this plot, when tTh is less than around 2.2, d=0, when thereafter, d=tTh. The changing pattern is similar to, but little more drastic than, that of exponential distributions. The highest incorrect handover decision probability is at around 40%. Fig. 4 (c) plots the handover reduction rate where d is the solution of eq. (3.6). In this figure, when tTh is less than around 2.2, the reduction rate is 0 because of the solution of the equation (3.6) is 0. After that point, the handover reduction rate increases in same pattern as the cdf of tR.

Fig. 4.The numerical results for tR~Γ(3.5, 1.1275): (a) incorrect handover decision probability according to tTh and d (b) incorrect handover decision probability according to tTh (c) handover reduction probability according to tTh

Fig. 5 shows the numerical results of Weibull distribution for the eq. (4.4). We can see that all plots are very similar to those of the Exponential distribution case. This is because the eq. (4.2) and (4.4) have very similar shapes to each other. Hence, the above results can be explained in the same manner as in the Exponential distribution case.

Fig. 5.The numerical results for tR~WEB(3.8, 0.9965): (a) incorrect handover decision probability according to tTh and d (b) incorrect handover decision probability according to tTh (c) handover reduction probability according to tTh.

Fig. 6 shows the numerical results of Pareto distribution for the eq. (4.5). Since the pdf of Pareto distribution is monotonic decreasing, for all value of tTh, incorrect handover decision probability is minimized when d=tTh. The notable thing of here is that the changing speed is slower than in other distribution cases. That is why tR is more uniformly distributed (even at the range of few hours or few days) compared to other distribution cases. In other words, due to the long-tail property of Pareto distribution, the portion of short-residence time users is lower than other distribution cases. The long-tail property makes the effects of tTh weaken on Pr[v(tR,tTh,d)=0] and Rh. Therefore, the efficacy of delay based AC may be degraded in Pareto distribution case.

Fig. 6.The numerical results for tR~P(I)(0.183, 0.06): (a) incorrect handover decision probability according to tTh and d (b) incorrect handover decision probability according to tTh (c) handover reduction probability according to tTh.

 

5. Conclusion

In hierarchical cellular systems, reducing unnecessary handover is an important issue because many inter-tier handovers may cause significant burden to the macro base station. Therefore, some recently proposed handover schemes adopt the delay based AC which delays the macro → small cell handovers for pre-determined waiting time to prevent short-term residence time users being unnecessarily handed to the small cell. In such delay based AC, determining the proper delay parameter is important matter because if too long or too short delay parameter causes the system makes undesirable actions such as wrong allowances of unnecessary handovers, or wrong avoidance of necessary handovers. To quantify this issue, we introduce a new performance metric referred to incorrect handover decision probability which balances trade-offs between the occurences of the above two undesirable situations. By using the incorrect handover decision probability as the objective function, we express the proper delay parameter decision problem as an minimization problem that can be easily solved numerically. From the extensive numerical evaluations and probabilistic analysis, we find out that when the probabilistic distribution function of tR is monotonic, we do not have to solve the minimization problem. All we have to do is simply choosing the one between two candidates: 0 and tTh. This property will be a helpful reference when a network operator designs a delay based AC protocol for hierarchical macro-small cellular system. We hope that a future research discovers further useful properties about the incorrect handover decision probability functions especially for when an input distribution function is not monotonic.