Providing stochastic delay guarantees through channel characteristics based resource reservation in wireless network.
This paper is directed towards providing quality of service guarantees for transmission of multimedia traffic over wireless links. The quality of service guarantees require transmission of packets within prespecified deadlines. Oftentimes, bursty, location dependent channel errors preclude such deadline satisfaction leading to packet drop. Wireless systems need resource reservation to limit such deadline violation related packet drop below acceptable thresholds. The resource reservation depends on the scheduling policy, statistical channel qualities and arrival traffic. We choose Earliest Deadline First as the baseline scheduling policy and design an admission control strategy which provides delay guarantees and limits the packet drop by regulating the number of admitted sessions in accordance with the long term transmission characteristics and arrival traffic of the incoming sessions. We analytically quantify the stochastic packet drop guarantees provided by the framework, and show using simulation that the design results in low packet drop.
INTRODUCTION
Third generation wireless packet networks will have to
support real-time multimedia applications. The real-time
applications need Quality of Service (QoS) guarantees from
the network. One of the most important QoS requirements
is the packet delay, which specifies the upper bound on the
delay experienced by every packet of the application. For
most of the real-time applications packets delayed beyond
certain time are not useful. Further, the tra#c characteristics
and the delay requirements of various applications are
di#erent. In this heterogeneous environment, the challenge
is to design a methodology that allows us to decide whether
the required QoS can be guaranteed. In this paper, we focus
on designing such a methodology for a single hop wireless
packet network. Obtaining an e#cient solution to the one
hop problem is an impotent preliminary step toward solving
the problem for multi-hop wireless packet networks like
ad-hoc networks.
Real time tra#c often associates a service deadline with
every packet. If the packet is not served before the dead-
line, then the corresponding information loses its utility, and
the packet must be dropped. It is well known that earliest
deadline first based scheduling minimizes delay violations
and thereby minimizes packet drops[24]. However, the actual
amount of this packet drop depends on the tra#c load,
bandwidth resources and the transmission conditions, and
this amount may become unacceptable if the tra#c load is
not regulated. In other words, an e#cient admission control
framework is required to ensure that su#cient amount of
resources are available to meet the packet drop constraints
of the admitted session. The framework will depend on the
scheduling policy, as the resource utilization is di#erent for
di#erent scheduling policies. We choose Earliest Deadline
First (EDF) as an appropriate scheduling strategy on account
of its loss optimality properties, and propose an admission
control framework which caters towards EDF.
Sessions arrive with specific deadline requirements and estimated
channel statistics. The admission control frame-work
admits a session only if the deadline requirements of
the incoming session can be met with a high probability.
This decision depends on the tra#c loads and channel characteristics
of the existing sessions, and also those of the in-coming
session. Thus designing such a framework will involve
quantifying delay of any given session in terms of arrival
process and channel characteristics of all the contending
sessions. The key contribution of the paper is to provide
such a quantification, and thereafter present an admission
control condition which exploits the statistical multiplexing
of tra#c load and channel errors of the existing sessions so
as to reduce the overall packet drops of the admitted sessions
to acceptable values. We corroborate our results using
analysis and extensive simulations.
Admission control schemes have been studied extensively
in the wireline case[29]. However these schemes do not
counter the detrimental e#ects of location dependent and
bursty channel errors. Admission control conditions need
to specifically consider channel statistics while taking admission
control decisions, and reserve additional resources
for guaranteeing the desired QoS in spite of channel errors.
Further location dependent channel errors imply that the
channel may be accessible to some users but not to others
because of the di#erent fading characteristics, and thus admission
control decisions will be di#erent for di#erent ses-
sions, even if the desired delay guarantees and the tra#c
load are the same.
The existing research in admission control in cellular networks
focusses on resource reservation for providing promised
QoS to the mobile users during hand-o#s [1, 2, 3, 15, 23, 16,
26, 27, 28, 17, 7]. These schemes assume the knowledge
of resources to be reserved to provide the desired QoS and
then obtain the good balance between call dropping and call
blocking via resource reservation. In this paper, we focus on
quantifying the resources required to provide packet delay in
presence of channel errors.
Most of the prior wireless scheduling work [5, 19, 20, 21]
obtains delay guarantees for sessions that do not experience
channel errors. In [19, 20], authors have obtained the
worst case delay bound for the sessions with channel errors.
However, these bounds hold only for Head of Line (HoL)
packets, in other words no bound has been provided for the
overall delay experienced by the packet. Another area extensively
explored is that of fair scheduling [4, 6, 10, 12,
14, 25]. The main objective in this branch of research has
been to distribute available resources fairly among the flows
[5, 19, 21, 22, 20], which is important for transmitting data
tra#c. Major concerns for transmission of real time tra#c
such as deadline expiry and related packet drop have not
been addressed though.
The main contribution of this paper can be summarized
as follow. We propose a channel statistics aware admission
control mechanism for EDF scheduler in wireless case. The
proposed mechanism guarantees delay bounds to the admitted
sessions with a high probability in spite of channel errors.
The deadline violation related packet drops are correspondingly
probabilistically upper bounded.
The paper is arranged as follows. We describe our system
model in 2. In section 3 we present the admission control
algorithm for EDF scheduler. In section 4 we present the
simulation results and discussion. We conclude in section 5.
2. SYSTEM MODEL
In this section we define our system model and specify our
assumptions. A system that we consider is shown in Figure
1. Further, we assume that a sender node S is transmitting
packets to several receivers in its communication range
via error-prone wireless channels. The sender node has an
admission control scheme and EDF scheduler. We assume
R
R
R
R
R
Arrivals from
Outside World24
Node
Transmission Range of
Sender

Figure

1: Figure shows a sender node S and its receivers
to R5 . Sessions arrive at the sender from
outside world and seek to transfer data to one of
the receivers. We do not preclude a possibility of
multiple sessions between the sender and a receiver.
Dotted circle represents the transmission range of
the sender.
that the sessions 1 arrive at the sender dynamically and seek
admission. Each arriving session specifies its required delay
guarantee and tra#c characteristics. Further, as we describe
below, each of the receivers periodically communicate
the estimates of long term channel error rate to the sender.
Using these parameters and the information about the available
resources, admission control mechanism at the sender
node decides whether the desired delay can be guaranteed 2
If the required packet delay can be guaranteed in the sys-
tem, then the session is admitted, otherwise it is blocked.
Packets that belong to the admitted sessions are served as
per EDF scheduling. We next describe each component of
our system model in detail.
We assume slotted time axis, where each time slot is of
unit length. Every packet has unit length. We assume leaky
bucket constrained sessions [9], i.e. the total data arriving
from a typical session i in any duration # is less than or
equal to #
replenishment rate. Wireless channel for a session is
either good or bad. In good channel state, the probability
of correct reception is 1, while in bad state the probability
is 0. There can be many sessions between the sender and
a given receiver. We allow the possibility that di#erent sessions
between the sender and a receiver can have di#erent
channel characteristics. This scenario arises if di#erent coding
and/or power control schemes are used for the di#erent
sessions.
We note that all the receivers are in the transmission range
of the sender. Hence, each receiver can receive all the transmissions
from the sender (including transmissions for other
receivers). Depending on the quality of reception, a receiver
can estimate its channel state parameters. So, we consider
a scenario where a receiver estimates its long term channel
error rate by observing the quality of receptions. We as-
1 A session is a stream of packets pertaining to a single application
that have to be transmitted from the sender to a
specific receiver. We do not preclude a scenario, where multiple
sessions exist between the sender and a certain receiver.
All guarantees are in a stochastic sense, i.e., a required
delay must be guaranteed with a high probability. We will
omit "with high probability" for brevity.
sume that receivers communicate the estimates of the long
term channel error rates to the sender periodically. Sender
uses these estimates and the leaky bucket parameters of the
arrival process to make the admission control decisions.
The EDF scheduler assigns a deadline to a packet as and
when it arrives. The deadline of a packet is the sum of its
arrival time and the required delay guarantee. In wireline
case, EDF schedules packets in the increasing order of their
respective deadlines. But in wireless case, to utilize channel
bandwidth e#ciently, packets that belong to sessions with
good channel should be scheduled. We assume a channel
state aware EDF scheduling where the packet with the earliest
deadline amongst those which experience good channels
is scheduled. The underlying assumption is that the scheduler
knows the channel state for each session in the beginning
of each slot. Such knowledge may not be feasible in real
systems. However channel state may be predicted given the
transmission feedback in the previous slot. We incorporate
a prediction based EDF strategy in our simulations.
We describe the proposed admission control scheme in the
next section.
3. ADMISSION CONTROL
In this section we present an admission control algorithm
for channel state aware EDF scheduler in wireless case. There
has been extensive work in admission control algorithm for
EDF scheduler in wireline case[11, 13, 18]. These algorithms
does not apply to wireless case as they do not accommodate
channel errors. We intuitively explain how channel errors
can be taken into consideration while making admission
control decision. This will enable the generalization of wire-line
admission control strategies for operation in the wireless
case.
Let us consider a case, where V is the maximum number
of erroneous slots in a busy period, where erroneous slot is
a slot in which at least one of the sessions have bad chan-
nel. A busy period is defined as the maximum contiguous
time interval in which packet from at least one session is
waiting for transmission. As shown in Figure 2, in the duration
of channel errors sessions can loose service that they
would have gotten if the channel were good. The system
has to compensate for the lost service. This compensation
causes additional delay in the wireless system. When the
erroneous slots are bounded above by V in any busy period,
the maximum compensation that a system needs to provide
is also bounded above by V . Hence, intuitively the excess
packet delay over the delay in the system with perfect channel
should be no more than the total number of erroneous
slots in a busy period. Further, a system in which channel
is always good for all the sessions is equivalent to the
wireline system. Hence packet delay for a session in wireless
case should be equal to the sum of packet delay in a
wireline case and V . We shall refer to the delay under EDF
in wireline system as WEDF-delay. Hence, if D i is the required
packet delay for the session i, then it su#ces to check
whether can be guaranteed in the wireline system
under EDF. This observation will allow us to use the admission
control schemes designed for wireline system in wireless
systems. Formally we state the following result.
Proposition 1. Every packet of all the admitted sessions
meets its deadline if the total number of erroneous slots in
a busy period is bounded above by V . Consequently, there isp (1)
(2)
(1)p (1)
(2)
(2)
(2)(a)
(b)

Figure

2: Example to show that the compensation
taken by one session a#ects the delay guarantees
of all sessions. Arrows pointing towards and away
from the axis represent packet arrivals and depar-
tures, respectively. p (i)
th packet from i th
session. V1 indicates a time slot in which session 1
has a bad channel. We note that the scheduling is
as per EDF. Consider two sessions 1 and 2. The delay
requirement for packets of session 1 and 2 are 3
and 2, respectively. We note that these delays can
be guaranteed with the perfect channel assumption.
In (a) After V1 , p (1)
takes immediate compensation
and as a result p (2)
experiences additional delay of 1
unit. In part (b), session 1 does not seek immediate
compensation after V1 , but it takes it eventually.
As a result packet p (2)
again experiences additional
delay of 1 unit. Hence as a result of channel error
of one unit for session 1, guaranteed delay for both
the sessions is increased by 1 unit.
no packet drop in the system.
The proof for the proposition is given in [8].
In wireless case, the channel errors are random. Hence,
the number of erroneous slots in a busy period are not
bounded in general, and thus the above proposition can
not be applied directly. Further, the length of busy period
and the number of erroneous slots in a busy period are
inter-dependent, i.e. the busy period length depends on the
number of erroneous slots in the busy period and vice versa
(refer to Figure 3). In spite of these issues, now we will show
how the above proposition can be generalized to account for
random channel errors. We observe that Proposition 1 can
be extended simply to obtain the packet drop probability
Pd . To illustrate the point, we fix some value for V . The
choice of V is not trivial and as we will show later appropriate
choice of V allows us to obtain desired balance between
session blocking and packet drop. Now, lets assume that the
probability of erroneous slots exceeding value V in a busy
period of length Z is Pd . So, from Proposition 1 it clear
that with probability Pd all the deadlines will be met and
system will not have packet drop. Now, the question we
need to investigate is "How to compute the drop probability
Pd ?" For doing this, first we investigate a relation between
the number of erroneous slots and the busy period length
Z. We note that if the erroneous slots in a busy period were
bounded by V , then the maximum length of busy period (Z)
time
time
Work in
the system
Channel Errors

Figure

3: Figure demonstrates the e#ect of channel
errors on the length of the busy periods under
EDF. Only the bottom figure experiences channel
errors, which lengthen its busy period duration by
7 additional time units (from 12 to 19).
under EDF scheduling is given by the following equation.
if
where C is the set of admitted sessions. The above expression
can be explained as follows from the definition of the busy
period. The total work which arrives in the system during
a busy period must be served during the same busy period.
Hence, Z the maximum length of a busy period satisfies
hand side of the equation
is the maximum data that can arrive in duration Z and
right hand side is the minimum service that the sessions will
obtain in the busy period. Thus equation 1 follows. Now,
given this busy period length, we can obtain the probability
that the total number of erroneous slots will exceed the value
(denoted by Pd ), using the channel parameter estimates
obtained from the receivers. We will show the computations
in the Section 3.1. We note that the value of V can be chosen
so that Pd is small.
Now, the drop probability in the system depends on the
value of V . If V is large(small) then the drop probability
is small(large). But V can not be made arbitrarily large
in order to reduce the drop probability, since increasing V
would increase the session blocking. The packet delay in
wireless system is WEDF-delay plus V , and hence increasing
would require a decrease in WEDF-delay, which can
be guaranteed only if the system has low tra#c load. The
quantity V can be looked upon as additional resource reservation
in anticipation of channel errors. The system does not
have any packet drop as long as the total erroneous slots in
a busy period are not more than the reservation V . Thus,
the choice of V is a policy decision or V can be adjusted
dynamically so as to cater to the system requirement.
Based on the above discussion, we propose the following
admission control algorithm. The proposed admission
control algorithm guarantees the packet drop probability
smaller than the acceptable packet drop probability P . The
pseudo code for the algorithm is given in Figure 4.
The proposed algorithm works as follows. Whenever a
new session arrives, sender node computes the new busy period
length Z and the probability Pd that the total number
of erroneous slots will exceed the fixed value V . If the drop
Procedure Admission Control Algo1()
begin
Fix V
When a new session arrives do the following
Compute new busy period length Z using equation (1);
Using the channel characteristics compute the probability P d that
the total number of erroneous slots exceed value V in the busy
period of length Z;
/* The probability that the total number of channel errors exceeding
V in a busy period of length Z (P d ) is greater than the
required packet drop probability P */
Block the session;
else
Check admission control under EDF in wireline case with D i -V ;
can be guaranteed in wireline system then
Admit the session;
else
Block the session;

Figure

4: Pseudo code of a general admission control
algorithm for an error-prone wireless channel
probability Pd is greater than the permissible value P , then
it blocks the session, otherwise it checks if the delay D i -V
can be guaranteed under WEDF. If delay D i - V can be
guaranteed the session is accepted, otherwise it is blocked.
In the following section we discuss the analytical computation
of the probability Pd that the total number of channel
errors in the duration Z will exceed value V .
3.1 Numerical Computation of Drop Probability
Pd
In this section we compute the probability that the total
number of erroneous slots in any duration Z exceeds the
value V (Pd ). Recall that Pd is an upper bound for the
packet drop probability. We consider the following analytical
model. We assume that the system has admitted N
sessions. For each session, we assume a two-state Markovian
channel error model as shown in Figure 5. The two
states are good and bad. Let the transition probability from
good to bad and from bad to good be # and #, respectively
for each session. Furthermore, we assume that the channel
state processes are independent.
The number of sessions for whom the channel is in the bad
state is a markov process with state space {0, 1, . , N}. The
transition probabilities for this Markov chain can be given
as follows.
Good Bad
a
1-a

Figure

5: Figure shows two state Markov process
for the channel state process.
Packet
Probability
Allowed Compensation (V)
Packet Drop Probability Obtained by Numerical Compution

Figure

Figure shows packet drop probability for
various values of busy period length (Z) and parameter
). The total number of active sessions are
assumed to be 10. Further, we assume that each
session has


u=i


We observe that the defined Markov chain is (a) finite
state space (b) aperiodic and (c) irreducible. Hence using
transition probabilities given in equation (2) and (3), we can
compute the steady state distribution. In state 0, all the
sessions have good channel. The drop probability Pd is the
probability that in Z slots Markov process visits state zero
less than Z -V times. This probability can be obtained using
computational techniques. In Figure 6 we present some
numerical results. We note that the numerical results are
consistent with the intuition. In particular, the packet drop
probability reduces as the value of V increases and increases
as the length of busy period increases.
In the above discussion, we have assumed that the transition
probabilities for all the sessions are identical. If this
is not the case, the number of sessions with a bad channel
state is not markovian. Thus the system can only be represented
by an N-dimensional vector, where each component
denotes the channel state of individual sessions. Similar to
the previous case, the Markovian structure can be exploited
to obtain Pd numerically.
The numerical computations involve calculation of steady
state distribution, which can be obtained by solving the ma-
Procedure Admission Control Algo2()
begin
When a new session i arrives do the following
Compute new busy period length Z using equation (1);
Obtain new value of channel errors in the busy period of length Z
/* the value of channel errors if i were admitted
than a maximum allowed value (V ) */
Block the session
else
Check admission control under EDF in wireline case with D i -V ;
if (D can be guaranteed in wireline system) then
Admit the session;
else
Block the session;

Figure

7: Pseudo code of a general admission control
algorithm for an error-prone wireless channel
trix equation. This can become computationally prohibitive.
Hence we propose a simpler approach to provide packet delay
in presence of channel error using EDF scheduler in the
following subsection.
3.2 Simplistic Approach
The computationally simple alternative approach is based
on the following observation. If # i is a long term channel error
rate for the session i then the number of erroneous slots
for the session in su#ciently long interval L is close to L# i
with high probability. This observation follows from the
Strong Law of Large Numbers or ergodicity property of the
Markovian channel error models, e.g. Gilbert-Elliot model.
Each receiver can estimate the required long term error rate
# i from the previous transmissions of the sender, and communicate
this estimate periodically to the sender node.
If the maximum length of a busy period, Z is small, then
the total number of erroneous slots must be few and hence
the packet drop rate is low. We need to carefully upper
bound the total number of erroneous slots for large values
of Z. If Z is su#ciently large, then Z
the total number of erroneous slots in a busy period with
a high probability. Using this computationally simple estimate
for the number of erroneous slots in the busy period, we
propose a new admission control algorithm, which uses the
same intuition as the previous one, but di#ers in computing
the estimate for the packet drop probability. Recall that in
the previous algorithm (refer Figure 4), we have explicitly
computed the packet drop probability Pd and then we have
ensured that the computed drop probability is smaller than
the required value P . In this scheme, we compute the average
number of erroneous slots in a busy period of length
Z based on the long term channel error rates (denoted by
If the computed number of erroneous slots V # is less
than the fixed value V , we assume that the system will not
have packet drop with high probability. Pseudo code for the
algorithm is given in Figure 7.
The proposed algorithm works as follows. Whenever a
new session arrives, sender node computes the new busy period
length Z and the total long term channel error rate if
the arriving session were admitted. If the expected total erroneous
slots Z
blocks the
session, otherwise it checks if the delay D i -V can be guar-
0Session
Blocking
System Parameter (V)
Blocking Performance of EDF

Figure

8: Figure provides session blocking performance
of EDF with perfect channel knowledge and
the proposed predication based scheme. T denotes
the inter-arrival time for the sessions.
anteed under WEDF. If delay D i -V can be guaranteed the
session is accepted, otherwise it is blocked. In the following
section we present the simulation results.
4. SIMULATION RESULTS AND DISCUS-
SION
In this section, we evaluate the packet drop and session
blocking for the proposed admission control algorithm for
EDF schedule. We assume that the sessions arrive at a fixed
node in a Poisson process with rate #. An arriving session
specifies its leaky bucket parameters. We assume bucket
depth # and token replenishment rate # to be uniformly distributed
between 0-10 packets and 0-0.1 packets per unit
time, respectively. The required delay guarantee for the session
is assumed to be uniformly distributed between 5-100
time units. We model error prone wireless channel as an
ON-OFF process. The transition probabilities from good to
bad and bad to good are 0.001 and 0.1, respectively. These
channel parameters correspond to Raleigh fading channel
where the mean fade duration is slots and the channel
is good for 99% of the total time [24].
We have performed simulations for two systems (a) when
the sender has perfect knowledge of channel state of each
session in the beginning of the slot (b) when sender predicts
the future channel state based on the outcome of the present
transmission. We note that in practice it is di#cult to obtain
the perfect knowledge of instantaneous channel state for
every session and hence option (b) is more suited for practical
applications. In (b), we use simple two step prediction
model, where if the current transmission is successful the
sender assumes that the channel state for the session will
be good in the next slots, but if the communication is not
successful then sender assumes that the session will have a
bad channel for the next 1
slots. We note that 1
is the
expected number of slots for which a session will have erroneous
channel, given that it has bad channel in the current
slot.

Figures

show the performance of the designed
admission control scheme for the EDF scheduler in0.0020.0060.01
Packet
System Parameter (V)
Packet Drop Performance of EDF with Perfect Channel Knowledge

Figure

9: Figure provides packet drop performance
of EDF when the scheduler has the perfect knowledge
of channel state for every session before packet
transmission.

Table

1: The table investigates the reduction in
packet drop brought about by additional resource
reservation. The chosen channel parameters are
and the EDF scheduler has instantaneous
knowledge of channel state before packet
transmission
Packet Drop with
resource reservation
Packet Drop without
resource reservation
200
wireless system.
We note that the session blocking curve is cup-shaped (see

Figure

8). For small values of V , the system reserves less
resources for compensating for channel errors, and hence can
only accommodate a few sessions with low long term channel
error rate (otherwise Z
when V is high the session blocking is high again as the
guaranteed delay is the sum of the WEDF delay and V, and
hence the former must be small so as to compensate for the
large value of the latter. The WEDF delay is small only if
a few sessions are admitted.
The packet drop performance is intuitive. When the value
of V is small the packet drop is higher and the packet drop
goes to zero as V becomes large. We note that the overall
packet drop performance of the system is better than the
calculated packet drop probability (see Figures 9 and 10).
This is because the numerical computations do not account
for the service given to other sessions when one session has
a bad channel, and hence only upper bound the packet drop
rate.

Tables

1 and 2 demonstrate that the packet drop can be substantially
reduced by reserving additional resources. We examine
the drop performances of two schemes: (a) the scheme

Table

2: Comparison of packet drop performances
with and without resource reservation for the prediction
based EDF scheduling.
Packet Drop with
resource reservation
Packet Drop without
resource reservation
200
300 0.178824 0.5377670.0020.0060.01
Packet
System Parameter (V)
Packet Drop Performance of EDF with Channel Predication Scheme

Figure

10: Figure provides packet drop performance
of EDF with the proposed two-step prediction
scheme.
we propose which reserves additional resources for compensating
for channel errors another scheme
which does not reserve any resources and admits sessions as
long as the WEDF delay is less than the required guarantee,
disabling the verification of other admission control criteria.
The latter has substantially higher packet drop.
5. CONCLUSIONS AND FUTURE WORK
In this paper, we have proposed connection admission control
algorithms to provide stochastic delay guarantees in a
single hop wireless network. EDF is used as a baseline sched-
uler. We have argued that the wireline admission control solutions
are not suitable for the wireless case as they do not
take into consideration the channel errors which can result
in high packet drop on account of deadline expiry. In the
proposed approach, we consider channel characteristics of
the sessions while taking admission control decisions. As a
result, we can provide the delay guarantees with the desired
packet drop probability. The guarantees can be provided
only if the EDF scheduler uses instantaneous channel states
in the scheduling decision mechanism. The channel states in
the previous slots can be used to predict the instantaneous
channel states if the latter is not known. The analytical
guarantees do not hold in this case, but extensive simulation
results indicate low packet drop.
The proposed admission control algorithms assume EDF
as a baseline scheduler. We are currently looking at admission
control schemes for other important scheduling disciplines
like fair queueing disciplines. Further, in this paper
we have only been able to upper-bound the overall packet
probability. No bound for the packet drop of individual
sessions is obtained. It is entirely possible that excessive
channel errors of one session deteriorate the packet drop rate
of other sessions. A framework which guarantees individual
packet drop rates is a topic for future research. Also, it
has been assumed throughout that the sender receives instantaneous
feedback after every transmission. We plan to
investigate the e#ects of delayed feedbacks.
6.



--R

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