Abstract— Two-tier cellular networks provide an enhanced use of the networks' resources for both high and low speed users. However, they cause an increase in the number of handoffs between cells due to having smaller cell sizes in the microcell tier. An effective approach used to prevent the dropping of ongoing calls in a network is delaying these calls in a queue until a channel becomes available. In this paper, we propose a new Markov model for a two-tier cellular network having a FIFO queue in the microcell tier. The performance of the model is then compared with those of a previously proposed model having a queue in the macrocell tier and the effect of having a queue in the microcell or macrocell on both high and low speed users is observed.
Keywords—Blocking probability, FIFO queue, Markov chains, Two-tier cellular networks.
I. INTRODUCTION
o design an effective cellular system, it is required to determine the Quality of Service (QoS). A common measure of the QoS is the handoff call blocking probability, which is the probability that an ongoing call is dropped due to the unavailability of free channels in the cellular network. Wireless cellular networks consist of a number of cells in which their sizes depend primarily on the population and the geographical area. For high-populated areas, cells with smaller sizes are more preferable than larger sizes to accommodate the large number of mobile users. However, this causes more blocking probability for high speed users (i.e. in a car) because of the frequent handoff from one cell to another.
A single-tier cellular network can reduce the handoff call blocking probability by reserving channels in the cell exclusively for handoff calls or giving higher priority to the handoff calls over the new calls. Queuing handoff calls is another way to improve the system performance by delaying the call until a free channel is available. These methods improve the handoff call blocking probability; however, they cause an increase in the new call blocking probability. In addition to this, the number of channels available in the
Manuscript received March 23, 2004.
Tara Salih is with the Computer Engineering Department at Fatih University, Istanbul, Turkey (phone: 8890912; fax: +90-212-8890906; e-mail: [email protected]).
Kemal Fidanboylu is with the Electroncis Engineering Department at Fatih University, Istanbul, Turkey (email: [email protected]).
network may not be enough to handle the large number of mobile users.
A multi-tier cellular network can improve the system performance by using the above methods. In addition to this, it can provide more channels to the network and based on the mobility of the mobile users, calls can be delivered to the appropriate layers. Cell splitting improves the cellular network capacity by increasing the number of cells and channels which a mobile user can access through the network. However, having smaller cells increases the cross rate of mobile users between these cells. Multi-tier cellular networks reduce the cross rates by having larger cells overlaying the smaller cells, and the high speed users are assigned to the layer with larger cell sizes.
Many studies have been done to develop wireless cellular networks that provide the best performance and efficiency. Handoff calls have been the main factor in evaluating the performance of a cellular network. Some models such as those mentioned in [1], [2], and [3] used guard channels for handoff calls to decrease the blocking probability. Guard channels are channels exclusively reserved for handoff calls. However, other models such as, [4] and [2], used queues to delay handoff calls until a channel becomes available. A model with a priority queue in the macrocell tier was proposed in [5]. The high speed users handoff calls in the queue had higher priority when a channel is released. In [6], a two-tier cellular network having a FIFO in the macrocell tier was proposed. The proposed network took into account the cell size, the cell dwelling time and the mobility of the users to obtain the queue time of each type of user. Since the queue is in the macrocell tier, both the high and low speed user have access to the queue.
The performance of a two-tier cellular network with a queue in one of its tiers depends on the distribution of the users in the geographical area of the network. In our paper, we propose a model of a two-tier cellular network with a FIFO queue in the microcell to study its effect on the users. We compare the results with those obtained from the previously proposed model having a queue in the macrocell tier. In addition, we compare our results with those of a two-tier network having no queue in any two-tier and display the improvement in having a queue in the network.
II. SYSTEM DESCRIPTION
In this paper, a two-tier cellular network with a FIFO queue in the microcell is proposed. The proposed model is valid for networks covering a large geographical area. The low and high speed users are assigned to the microcells and the macrocells, respectively. The radius of the microcell is
A Comparison of the Performance of Two-Tier
Cellular Networks Based on Queuing Handoff
Calls
Tara Salih and Kemal Fidanboylu
smaller than the macrocell, and an integer number of microcells are covered by one macrocell.
We have assumed that once a low speed user call is overflowed to the macrocell, it cannot return back to the microcell and when a low speed user becomes a high speed user the call is overflowed to the macrocell. Calls overflow from the microcell to the macrocell also when the low speed user’s new or handoff call cannot find a free channel in the microcell.
A channel is released under two conditions: when a user voluntarily terminates the ongoing call and when a handoff call completes either with success or failure.
A handoff call is blocked when it cannot find a free channel in the desired cell. This happens due to certain factors, such as, the queue is full or the queue time assigned to the users is too short for the call to wait for a channel to be released. A new call is blocked when it cannot find a free channel in the cell.
A. Model parameters
We assume that the cells are circular in shape. Table 1 shows the parameters we have used for modeling the cellular network.
The arrival rates of new calls and handoff calls for both low and high speed users are assumed to be Poisson processes. The cell dwelling time is the time a mobile user spends in a cell before it is handed off to another cell. It depends on the speed of the mobile user and the size of the cell. The cell dwelling time can be calculated as shown in [1] as follows:
v
r
d2
1
S
P
(1)where r is the radius of the cell and v is the speed of the mobile user.
The queue time is the time the handoff call remains in the queue. In [5], it is shown that the mean queue time depends on two parameters
(a) The mean cell dwelling time.
(b) The maximum cross-distance M, over the overlapping zone between two cells.
Hence, queue time = ( M /100) x cell dwelling time.
The average holding time, the mean cell dwelling time and the mean queue time for both low and high speed users are assumed to be negatively exponentially distributed.
B. Analysis of the microcell tier
The first part of the analysis corresponds to the microcell tier represented by a Markov chain with a FIFO queue and is analyzed as in [7] and [8]. Fig. 1 shows the state s(i), where i denotes the number of low speed users in the microcell. We assume that the number of channels, c, equals 3 and the queue size, Q, equals 2 as shown in Fig. 1.
Fig. 1. State transition diagram for a microcell with 3 channels and a queue size of 2.
In the above transition diagram, m and q are given by
dl
m
P
P
andq
P
P
ql , respectively. By solving the Markov chains, we find that the state probability P(i) is similar to the results obtained in [8] as follows:>
@
° ° ¯ ° ° ®
c i j dl ql c dl c i lh c lh i dl i lh j c c P i P i P 1 ln ln ! 0 ! 0P
P
P
P
P
P
O
O
O
P
P
O
O
(2) Since1 0
¦
c i iP , then P(0) can be expressed as
>
@
1 1 1 1 ln ln ! ! 1 0 » » » » ¼ º « « « « ¬ ª¦
¦
c i Q c c i c i j ql dl c dl c i lh c lh i dl i lh j c c i PP
P
P
P
P
P
O
O
O
P
P
O
O
(3) The blocking probability for new calls,P
n, is given by¦
cq c i n Pi P (4)The blocking probability for handoff calls,
P
h, is given by¦
Q c i h Pi P (5)The overflow traffic for low speed new calls,
O
ol and handoff calls,O
olh are calculated , as in [1], using the following equations n l ol NO
PO
(6) h hl olh NO
PO
(7)C. Analysis of the macrocell tier
The second part of the analysis corresponds to the macrocell tier without a queue. The system is analyzed using a Markov chain that contains the state s(i,j), where i and j are the numbers of low and high speed users in the system, respectively. The Markov chain model with 3 channels is shown in Fig. 2.
c
i
d
c
i
!
TABLE IMODEL PARAMETERS AND DESCRIPTIONS
Symbol Description
c Number of channels in each cell.
N Number of microcells that are overlaid by one macrocell
Q Size of FIFO queue.
O1 Arrival rate of new calls for low speed users.
Oh Arrival rate of new calls for high speed users.
Ohl Arrival rate of handoff calls for low speed users.
Ohh Arrival rate of handoff call for high speed users.
1/P Mean average holding time for both types of users. 1/Pdl Mean cell dwelling time for low speed users.
1/Pdh Mean cell dwelling time for high speed users.
1/Pql Mean queue time for low speed users.
Fig. 2. Markov model of the macrocell with 3 channels. The parameters involved in the Markov chain are defined as follows 2 L olh ol L
O
O
O
hh h HO
O
dl M1P
P
dh M2P
P
We define the following inclusion functions to find the equilibrium equation of the state probabilities using the approach presented in [9].
¯ ® else c j i q j i 0 1 , , D
¯ ® z else i q j i 0 0 1 , , E
¯ ® z else j q j i 0 0 1 , , G
The equilibrium equation for the state occupancy probabilities P(i,j,q) can be calculated as follows:
H j i P j i L j i P j i M i j i P M j j i P j i j i P jM j i iM j i H L j i ) 1 , ( ) , ( ) , 1 ( ) , ( ) 1 ) 1 )( , 1 ( 2 ) 1 )( 1 , ( )( , ( ) , ( ) 2 ) , ( 1 ) , ( ) )( , ( ( G E D G E D (8) The blocking probability for new calls,
P
bn, in the macrocell is given by¦
j c i bn P i j P (, ) (9)Since the macrocell does not have a queue, the blocking probability for handoff calls,
P
bh, in the macrocell can be calculated using the same equation forP
bn.The blocking probabilities for the overall system are calculated, as in [5]. Hence, let
P
bn_hand Pbh_h be the newand handoff call blocking probabilities for high speed user and
P
bn_l andP
bh_l be the new and handoff call blockingprobabilities for low speed users, respectively. Then, these probabilities can be written as:
bn h bn
P
P
_ (10) bh h bhP
P
_ (11) n bn l bnP
P
P
_
(12) h bh l bhP
P
P
_
(13) III. NUMERICAL RESULTS AND COMPARISIONS In this section, we show comparisons of the numerical results for the proposed two-tier cellular network having a queue in the microcell with those presented in [6]. Furthermore, the same results are compared with those obtained for a two-tier cellular network without having a queue. For the computation of the numerical results, we have assumed a homogeneous two-tier cellular network with one macrocell covering 7 microcells and each cell containing 3 channels. We assumed that the speed of the mobile users is pre-calculated so that once a call is originated the low speed users are assigned to the microcell tier and the high speed users are assigned to the macrocell tier. We used the same assumptions in [6] to obtain the results.Fig. 3 shows the effect of the new arrival rate on the handoff call blocking probabilities of low speed users for the three models. It is clear from the figure that the model with a queue in the microcell tier has a lower blocking probability than the others because the low speed users have access to the queue. In addition, the model with a queue in the macrocell tier also has lower blocking probability than the model with no queue. This is due to the fact that the low speed users after being overflowed have access to the queue along with the high speed users in the macrocell tier.
Fig. 3. Handoff call blocking probability of low speed users for the three different two-tier network models with different arrival rates of new calls.
The handoff call blocking probabilities for high speed users of the three models are compared in Fig. 4 when the arrival rate of new calls increases. The results show that, the model with the queue in the macrocell tier has a lower blocking probability than the others because the high speed users are able to access the queue in the macrocell when no free channels are available. In addition, the results for the model with no queue and the model with a queue in the microcell tier have the same blocking probabilities because the high speed users have no access to the queue in the
microcell tier. Hence, the call is not queued and therefore it is dropped.
From these results we can conclude that the low speed users have better performance than high speed users since the handoff calls have access to both of the queues whether the queue is in the microcell or the macrocell.
Fig. 4. Handoff call blocking probability of high speed users for the three different two-tier network models with different arrival rates of new calls.
Fig. 5 illustrates the effect of the arrival rate of new calls on the new call blocking probability for high speed users in two different cases: a queue in the microcell and a queue in the macrocell. In this figure, it is shown that the model with a queue in the microcell has a slightly lower blocking probability than the other model. This results from having a lower rate of overflow calls (new and handoff) to the macrocell tier due to the queue in its tier.
The results for the new calls of low speed users are similar to those of the high speed users when the arrival rate increases.
The new call blocking probability of low speed users versus the queue size for the three proposed models is shown in Fig. 6. From this figure, it can be observed that the new call blocking probability for low speed users is lower for the model with a queue in the microcell than the other models, because more new calls are able to overflow to the macrocell while the handoff calls are queued in the microcell.
Fig. 5. New call blocking probability of high speed users for two-tier cellular network models for different new call arrival rates.
The handoff call blocking probability of high speed users versus the queue size is illustrated in Fig. 7. The results obtained in this figure are similar to those obtained in Fig. 4.
Fig. 6. New call blocking probability of low speed users for the three different two-tier network models with different queue sizes.
Fig. 7. Handoff call blocking probability of high speed users for the three different two-tier network models with different queue sizes.
The new call blocking probability of high speed users as a function of the queue size for the three proposed models is shown in Fig 8. From this figure, it can be observed that the model with a queue in the macrocell has a higher probability than the other two models and increases until the queue size reaches the number of channels and then it becomes constant. On the other hand, the blocking probabilities of the other two models do not change with respect to the queue size.
Fig. 8. New call blocking probability of high speed users for the three different two-tier network models with different queue sizes.
III. CONCLUSION
Multi-tier cellular networks improve the performance of the system by adding additional channels that accomodate more users. A multi-tier cellular network with a queue in one of its tiers allow the handoff calls to wait in the queue for a limited amount of time until a channel is released. In this paper, we proposed a new markov model for a multi-tier cellular network with a queue in the microcell. We compared the performance of this model with those presented in [6]. From the results obtained, we conclude that the blocking probabilities of the high and low speed users are different in each model based on their distribution in the network, their mobility and the geographical area of the network.
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Tara Salih received her BS degree in Computer Science and Engineering
from Al-Isra University in 2000. She received her MS degree in Computer Engineering from Fatih University in 2003. She worked as a research assistant in the Computer Engineering Department between October 2000 and September 2003. She was appointed as an Instructor in the same department in October 2003. Her research interests are wireless mobile networking and 2G/3G wireless communication systems (GSM and UMTS).
Kemal Fidanboylu received his B.Sc. degrees in both Electrical
Engineering and Mathematics and M.Sc. degree in Electrical Engineering from University of Petroleum and Minerals in 1985 and 1987, respectively. He received his Ph.D. degree in Electrical Engineering from Virginia Polytechnic Institute and State University in 1991.
He worked as a research assistant in the Electrical Engineering Department at University of Petroleum and Minerals between 1985 and 1987. He also worked as a research assistant and then as a Visiting Assistant Professor in the Electrical Engineering Department at Virginia Polytechnic Institute and State University from 1987 to 1991 and from 1991 to 1992, respectively.
In 1992, he joined the Computer Engineering Department at Marmara University. He established the Electronics Engineering Department at the same univesity in 1993 and was appointed as the Vice Dean of Academic Affairs and the Director of Computer Training Certificate Program in 1994.
He joined Drexel University, Electrical Engineering Department as a Visiting Associate Professor in 1987 and was appointed as the Associate Director of Fiber Optics and Photonics Manufacturing Engineering Center.
In September 2000, he joined Fatih University, Electronics Engineering Department. In May 2001, he established the IEEE Fatih University Student Branch. Between June 2001 and March 2002, he served as the Director of Graduate Institute of Engineering and Sciences and between January 2002 and April 2004 he served as the Vice Rector for Academic Affairs. He is currently serving as the Acting Chairman of the Computer Engineering Department. His research interests are wireless communications, electronic circuits and fiber optics.
