Dec 12, 1993 - threshold, the network arranges for a hand-off to another port. The network asks all the surrounding ports to monitor the signal from the portable ...
1 Modeling the Channel Assignment Strategies for Hand-off and Initial Access for a PCS Network YI-BING LIN, SESHADRI MOHAN, AND ANTHONY NOERPEL BELLCORE MORRISTOWN, NJ December 12, 1993
Abstract The forced termination probability (the probability that a hand-off call is blocked) is an important criterion in the performance evaluation of the personal communication service (PCS) networks. The forced termination of an ongoing call is considered less desirable than blocking the initial access of a new call. This paper proposes analytic and simulation models to study the performance of different channel assignment strategies for hand-off and initial access. We observe that giving a priority to hand-off attempts over initial access attempts would dramatically improve the forced termination probability of the system without seriously degrading the number of failed initial access attempts. Some of our results are different from previous published results because our models capture features not considered in those studies.
1 Introduction A personal communication service (PCS) network [4, 5] is a digital communication network, which provides low power-high quality wireless access for PCS subscribers to the public switched telephone network (PSTN). The service area of a PCS network is partitioned into several sub-areas or cells. This paper assumes a fixed or quasi-static channel assignment [2] where a group of channels (time slots, frequencies, spreading codes or a combination of these) are assigned to each cell but the results are extensible to dynamic channel assignment schemes [3]. When a subscriber wishes to make or receive a phone call, the portable attempts to seize an available traffic channel for the connection. For some PCS radio systems, the portable launches an access request on a common signaling channel and is then directed to a traffic channel (DECT [7], or CT-2 Plus [15, 6]). In other PCS radio systems the access attempt is made directly on an available traffic channel (Bellcore WACS [1]). In the former case, there is a limited number of servers or transceivers in a port and when a port is blocked
Submitted to IEEE Trans. Veh. Technol
2
there is no transceiver for the signaling channel since they are all used for existing calls. In both cases there is usually no provision (either no channel, no protocol or both) for a portable to signal the need for a traffic channel to a blocked port and therefore access attempts cannot be queued by the network. If there is no available traffic channel or common signaling channel then the call is blocked. If there is an available traffic channel it is used to connect the call. The channel is released either when the call is completed or the portable (or the PCS subscriber) moves out of the cell. When a portable moves from one cell to another while a call is in progress, the call requires a new channel (in the new cell) to continue. This procedure of changing channels is called hand-off or automatic link transfer (ALT). If no channel is available in the new cell, then the call will be dropped or forced terminated. The forced termination probability is an important criterion in the performance evaluation of the PCS network. Forced termination of an ongoing call is considered less desirable than blocking of a new call attempt. Radio technologies for PCS typically support from 1 to 12 32-kb/s servers per port or cell. CT-2 Plus at the low end supports one transceiver per port, however, several ports can be collocated increasing the number of servers per cell. Bellcore’s WACS has 9 servers per transceiver and DECT has 12 servers per port or cell. There are typically between 20 and 50 servers for cellular mobile technologies which have a 25 MHz frequency allocation. In order to fit into the FCC’s 10 MHz allocations for PCS in the 2 GHz emerging technologies band, most air interface specifications will have to be re-engineered to have from 4 to 8 servers per port or microcell. In PCS networks it is expected that there will be more overlap of port coverage areas or microcells than that which exists for mobile networks with macrocells. Therefore, in most cases, there may be a “second best port” which a portable can successfully access either to complete a call or for an ALT, thus increasing the effective number of servers available to a portable in a cell. This effect is not studied in this paper. Three ALT strategies have been proposed for PCS networks: (i) Portable controlled hand-off, (ii) network controlled hand-off, and (iii) portable assisted hand-off. Portable controlled hand-off is the most popular technique and is employed by both the DECT and the WACS air interface protocols. In this method the portable is continuously monitoring the signal strength and quality from the accessed port and several ALT candidate ports. When some ALT criteria is met, the portable checks the best candidate port for an available traffic channel and launches an ALT request. Network controlled hand-off is employed by CT-2 Plus. In this method, the port monitors the signal strength and quality from the portable and when these deteriorate below some threshold, the network arranges for a hand-off to another port. The network asks all the surrounding ports to monitor the signal from the portable and report the measurement results back to the network. The network then chooses a new port for the hand-off and informs both the portable (through the old port) and the new port. The hand-off is then effected.
Submitted to IEEE Trans. Veh. Technol
3
Portable assisted hand-off is a variant of network controlled hand-off where the network asks the portable to measure the signals from surrounding ports and report those measurements back to the old port so that the network can make the determination as to where an ALT is required and to which port. This hand-off strategy is employed by the GSM mobile standard [14] but not by any candidate PCS radio system standards. In most proposed radio systems for PCS in the 2 GHz emerging technologies band, the ports are simple transponders or radio modems and all the intelligence resides in a radio port controller. It is presumed that the radio port controllers have the capacity to communicate with each other through the PCS network. Several ALT - initial access channel assignment schemes are described below (see [16] for a survey). The non-prioritized scheme (NPS) In this scheme, the port handles a hand-off call exactly the same as an originating call (i.e., the hand-off call is blocked immediately if no channel is available; see the first flowchart in Figure 1). This is the scheme employed by typical radio technologies which have been proposed for PCS in the emerging technologies frequency allocation at 2 GHz. The guard channel scheme This scheme is similar to NPS except that a number of channels or transceivers in each port are reserved for hand-off calls. The first-come-first-out (FIFO) scheme This scheme is based on the fact that adjacent cells in a PCS network overlay. Thus, there is a considerable area where a call can be handled by the ports in either of the adjacent cells. This area is called the hand-off area. The time that a portable moves across the hand-off area is referred as the degradation interval. The FIFO scheme is illustrated in the second flow chart in Figure 1. For portable controlled hand-off, when a portable with an ongoing call enters a hand-off area, it checks if there is a channel available on the new port. If not, this scheme requires that there be a way for the portable to signal to the new port its desire for an ALT and the hand-off call is buffered in a waiting queue, and the channel on the old port is used until a new channel is available. For WACS, a physical channel exists for the portable to signal a blocked port of the ALT attempt but the protocol is not currently specified so that this channel can not be used in this way. For DECT, if a port is blocked then no channel exists for the portable to make such a request. For network controlled hand-off systems, like CT-2 Plus, the old port can always make such a request to the new port but the protocol does not exist to inform the portable that it is a hand-off candidate but that its hand-off is on hold subject to the availability of a transponder. If a channel in the new cell is available for the ALT then the ALT actually
Submitted to IEEE Trans. Veh. Technol
4
occurs. If no channel is available after the portable moves out of the hand-off area (i.e., the degradation interval expires), then the call is forced terminated. In this scheme, when a channel is released, the port first checks if the waiting queue is empty. If not, the released channel is assigned to a hand-off call in the queue (see the third flow chart in Figure 1). The “next” hand-off call to be served is selected based on the queueing policy. In the FIFO scheme, the next hand-off call is selected in the first in first out basis. The measured-based priority scheme (MBPS) This scheme is similar to the FIFO scheme except for the queueing policy. MBPS uses a non-preemptive dynamic priority policy. The priorities are defined by the power level that the portable receives from the port of the new cell [17]. The hand-off area can be viewed as regions marked by different ranges of the power ratio. The network monitors the power levels of a queued hand-off call dynamically. For our purposes, we may view a hand-off call as having a higher priority if its degradation interval is closer to expiration. This is determined by the network to be the radio link with the lowest received signal strength and the poorest quality as measured by the portable. This implies that a mechanism exists for the portable to relay this information to the network over the failing radio link between the portable and the old port. A released channel is assigned to the queued hand-off call with the highest priority. Hong and Rappaport [10] proposed an analytic model for FIFO scheme assuming exponentially distributed degradation intervals. There are two major differences between Hong-Rapport model and the model developed in this paper. First, their traffic model is based on a special portable movement pattern. This paper generalizes the traffic model to accommodate arbitrary portable movement patterns. Second, we follow the exponential portable residual times proposed by Wong [18] to derive the exact values for the forced termination probability. On the other hand, Hong-Rappaport model approaches the special portable movement pattern by a Poisson process, which provides approximate results. Tekinary and Jabbari [17] proposed a similar analytic model for the FIFO scheme assuming normally distributed degradation intervals. The system was modeled by a Markov chain. Gnedenko and Kovalenko [9] pointed out that a Markov chain cannot model a queueing system with timeout periods which are not exponentially distributed. Another problem of the model is that the authors considered the hand-off traffic as an independent input parameter. In reality, the hand-off traffic is affected by the portable mobility, the call holding time distribution, and the originating call traffic. Yoon and Kwan’s study [19] made the same independent hand-off traffic assumption as Tekinary and Jabbari’s study. Furthermore, they used finite buffer queues (i.e., M=M=C=K
Submitted to IEEE Trans. Veh. Technol
5
Figure 1: Flow charts for hand-o queueing originating call arrival
channel available?
yes channel assigned
ongoing call
channel release
no call blocked
handoff call arrival
channel available?
yes channel assigned
ongoing call
yes
no
a channel is available for the call before it expires?
the call is inserted into the waiting queue
no
channel release
is the waiting queue empty?
yes the channel is idle
channel release
no
the channel is assigned to the ged to thein the waiting queue next call
the call is forced terminated
Submitted to IEEE Trans. Veh. Technol
6
system) to model the ALT - initial access channel assignment schemes. The behavior of the finite buffer system is very different from the timeout systems, and their models may not adequately approximate the behavior of the ALT - initial access channel assignment schemes. This paper proposes analytic models to study NPS and FIFO schemes. These channel assignment schemes are studied under two conditions. We assume 50 servers per cell for the mobile application so as to compare our results with previously published results [17]. We also show results for 10 servers per port to reflect the PCS environment. A simulation model is developed to validate the analytic models, and is used to study MBPS. Our results are different from the previous studies [10, 17] because our model captures the features not considered in the previous models.
2 Analytic Models This section proposes analytic models for the ALT - initial access channel assignment schemes. We first describe the traffic model, then describe the system models for NPS and the FIFO scheme, respectively. The guard channel call handling scheme can be directly extended from the FIFO queueing model as described in [10], and is not studied in this paper.
2.1 The Trac Model Suppose that a portable moves across K cell boundaries during a call holding time tc assuming that the call is completed. That is, K is the number of hand-offs before the call is completed. The call is referred to as a K -hand-off call. Following the technique we developed in [11], the probability K k is derived assuming that the incoming calls to a portable are a Poisson process, and the time the portable resides in a cell has a general distribution. We assume that the time interval between two consecutive phone calls to a portable is sufficiently larger than the call holding time such that the busy line effect does not occur [12] (i.e., there is no new phone call to a portable when it is in a conversation). Suppose that the portable resides in a cell R0 when a phone call arrived. During the phone call, the portable visits another K cells, and the portable resides in the j th cell for a time period tMj ( < j K ). Let tm be the time interval between the arrival of the phone call and the time when the portable moves out of R0 . Let tMi be independent and identically distributed random variables with the distribution Fm tMi and the density function fm tMi with mean = . Let rm t be the density function of tm , and the call holding time tc be exponentially distributed with the density function fc t e?t . Since the incoming phone calls are a Poisson process, from
Pr[ = ]
0
( )
()=
( )
1
()
Submitted to IEEE Trans. Veh. Technol
7
the random observer property [8] of a Poisson process,
rm (t) =
Z1
=t
= 1 ? Fm(t)
fm ( )d
(1)
The probability of a K -hand-off call is
Pr[K = k] = Pr[tm + tM1 + ::: + tMk?1 < tc tm + tM1 + ::: + tMk ] For k
1,
Pr[K = k] = =
Z1 Z1
Z 1 Z t0
t :::+tk fc (t)rm(t0)fm (t1):::fm(tk )dtdtk :::dt1dt0 tk =0 t=t0 +t1 +:::+tk?1 t0 =0 t1 =0 # Z 1 "kY Z 1 ?1 Z 1 ? t ? t ? t i 0 k e fm (tk )dtk e fm (ti )dti 1 ? e rm (t0)dt0 tk =0 t0 =0 i=1 ti =0 :::
+ 1+
(2)
From (1), we have
Z1 t0 =0
e?t0 rm(t0 )dt0
= =
Z1
e?t0
m
1 ? Fm(t )
dt0 0 t0=0 Z 1 ?t e 0 fm (t0)dt0 1 ? t0 =0
The Laplace-Stieltjes Transform for the distribution
f (s) =
Z1
t=0
(3)
Fm (t) is
e?st fm (t)dt
(4)
From (2), (3), and (4), we have
k ? Pr[K = k] = 1 ? fm () fm () 2
For k
1
for k
1
(5)
= 0, Pr[K = 0] = Pr[t < t ] Z 1 Z t0 = t t fc(t)rm(t )dtdt 0 = 1 ? 1 ? fm() 0
=0
=0
0
0
(6)
Submitted to IEEE Trans. Veh. Technol
8
Let pf be the forced termination probability. Consider a K -hand-off call which is connected as a new call attempted. Let J be the number of portable moves when the call is forced terminated or successfully terminated, where J K . The probability J j K k is
Pr[ = j = ]
81 0j =k1 > > p (1 ? p )j? j0 = < > : (1f ? pf )kf? j = kj k1 1
1
The the expected value of J for a ;E J K . For k > ,
1 [ j = 1] = 1 E [J jK
2
k -hand-off call For k
= 0; E [J jK = 0] = 0.
For
k
=
+ 2pf (1 ? pf ) + 3pf (1 ? pf ) + ::: + (k ? 1)pf (1 ? pf )k? + k(1 ? pf )k? k = 1 ? (1p? pf ) (7)
= k] =
pf
2
2
1
f
Let po be the blocking probability of the new call attempts. The expected number of hand-offs before a call terminates (either completes or is forced terminated) is po E J where (from (5), (6) and (7))
(1 ? ) [ ]
E [J ]
= = =
X
E [J jK
= k] Pr[K = k] X " 1 ? (1 ? pf )k # !
k , then a portable always completes the call before a move, and (pf )= = 0. Thus, pnc = po (i.e., the incomplete calls are blocked new call attempts). If >> , then a call never completes, and is eventually blocked, and (pf )= ! 1. Thus, pnc = 1. Hong and Rappaport [10] observed that pnc is more sensitive to po than pf . Their observation is not true in general. Equation (10) indicates that as = (the mobility to the call completion rate ratio) increases, the impact of pf on pnc increases, and the impact of po decreases. If
2.2 The System Model This section proposes analytic models for the non-prioritized scheme and the FIFO scheme.
2.2.1 The Non-prioritized Scheme =
In the non-prioritized call handling, pf po . The channel occupancy time is the minimum of the call holding time (note that the call holding time for a hand-off call has the same distribution as an originating call because of the memoryless property of the exponential distribution) and the remaining portable residual time. In other words, the density function fco t of channel occupancy time distribution is
()
fco (t) =
Z1
tc =t
fc (tc )fm (t)dtc +
Z1
tm =t
fc (t)fm (tm )dtm
= ( + )e?
t
( + )
(11)
Submitted to IEEE Trans. Veh. Technol The net traffic to the system is o
10
+ h . From the Erlang-B formula, (o + h )c ( + )cc! po = c X (o + h )i i i ( + ) i!
(12)
=1
Since po
= pf in the non-prioritized hand-off scheme, (9) is re-written as (1 ? po )o h = + po
(13)
The probability po can be obtained by assigning an initial value for h , and iterating (12) and (13) until the h value converges.
2.2.2 The FIFO Scheme Our system model for the FIFO scheme is similar to the one proposed by Hong and Rappaport [10]. The model is a direct extension of the timeout model described in [9], which assumes unlimited call sources. This model is appropriate when the expected number of portables in the cell is much larger than the number of channels. When the expected number of portables is small (but is still larger than the number of channels), other models must be considered [12, 13]. Assume that the degradation interval is exponentially distributed with mean = . Define the maximum queueing time of a hand-off call as the minimum of the degradation interval and the portable residual time. Thus, the maximum queueing time has the density function
1
fq (t) = ( + )e?( +)t
We follow a conservative assumption in [10], [17], and [19] that a hand-off call is blocked if it is not allocated a channel within the maximum queueing time. Note that the hand-off may not be blocked if the portable moves to another cell within the degradation interval. The impact of this assumption can be ignored if .
s( + ) s( + + 1)
s( + )
0
( + )
( + ) ( + )+ ( + )
s( + ) s( + ? 1)
0
s(n). Then 8 > (o + h )i ; > > < i!( + )i i = > (Y o + h )c nh?c ; > c > c !( + ) [ c ( + ) + j (
+ )] : j n?c
Let n be the steady state probability for 0
0
nc n>c
1
Since 0
+ + ::: + n + ::: = 1, we have 9? 8 > > > > 1 c ( + )i X = < X (Y o + h )c nh?c o h = 1 + i!( + )i + c > [c( + ) + j ( + )] > n>c c!( + ) > ; : i j n?c 1
1
0
=1
1
Since a new call is blocked when the system is in state originating call blocking probability is
po
=
1 X nc
s(n) (where n c) at its arrival, the (14)
n
Following the technique we developed in [13], the probability pf is derived as follows. Suppose that a hand-off call Ct arrives at time t when the cell is in state n (where n c j; j c; j ).
s( )
= +
Submitted to IEEE Trans. Veh. Technol
12
+
Consider the c j outstanding calls that arrive at the cell earlier than Ct. Suppose that among these c j calls, the first call leaves the queue 1 (i.e., either completes, expires, or leaves the cell) at time t tj . Then the density function for tj is
+
+
fj (tj ) = [c( + ) + j ( + )]e?[c(+)+j ( +)]tj
(15)
?1
+
If tj < , then at time t tj , Ct sees c portables in conversations and j hand-off calls waiting in front of itself. Now consider the first call leaves the queue among these c j calls (excluding Ct ). Suppose that the call leaves the queue at time t tj tj ?1. Because of the memoryless property of the call occupancy distribution and the maximum queueing time t0 ::: tj. distribution, tj ?1 has the density distribution fj ?1 as expressed in (15). Let Tj For a call Ct arrives at state n (n c j; j ), the probability that Ct is blocked is
+ ?1
+ +
s( ) = +
Z1
Pr[ < Tj js(c + j )] =
tj =0
Z1
=
::: :::
Z 1 Z t0
2 3 Y 4 fk (tk )5 fq ( )d dt :::dtj 2 j kj tj Y 4 [c( + ) + k( + )]e? c
:::+tj
+
0
t0 =0 =0
Z 1 Z t0
=
:::+
+
Thus, the forced termination probability pf is
pf
=
j
