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Service operators can enforce their own policies in providing user satisfaction. In this paper we consider a QoS- aware policy driven scheduling algorithm and its.
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Integrating Admission Control and Packet Scheduling for Quality Controlled Streaming Services in HSDPA Networks Joseph S. Gomes1, Hyeong-Ah Choi1 , Jae-Hoon Kim2 , JungKyo Sohn3, Hyeong In Choi3 1 Department of Computer Science, George Washington University, Washington, DC 2 Access Network & Mobile Terminal R&D Center, SK Telecom, Seoul, Korea 3 Department of Mathematics, Seoul National University, Seoul, Korea {joegomes,hchoi}@gwu.edu, [email protected], {jgsohn,hichoi}@snu.ac.kr

Abstract— High-Speed Downlink Packet Access (HSDPA) uses a shared forward link packet data channel that can achieve peak data rates upto 14.4 Mbps. The newly introduced features that are key to reaching such high rates are link adaptation, Hybrid ARQ (HARQ) and fast scheduling. The decision to admit new users is still taken by the Radio Network Controller (RNC); however the scheduling role has been moved to the base station (NodeB) for fast adaptability. Although in high speed cellular networks opportunistic scheduling can exploit multi-user diversity to maximize throughput, with the growing need for strict QoS guarantees for services such as streaming, gaming, and VoIP, a balance should be struck between maximizing throughput and providing user satisfaction. Service operators can enforce their own policies in providing user satisfaction. In this paper we consider a QoSaware policy driven scheduling algorithm and its interaction with the admission control mechanism at the RNC. We developed a dynamic HSDPA network simulator in OPNET with link adaptation, HARQ, fast scheduling and quality based admission control. Our simulations show that even with the presence of an admission controller at RNC, the well-known proportional fairness (PF) algorithm dismally fails to provide user satisfaction for streaming services, whereas our Strict Policy Scheduling (SPS) algorithm substantially increases user satisfaction as intended by the admission controller while providing a significant cell capacity gain.

This work was in part supported by the Access Network & Mobile Terminal R&D Center, SK Telecom, Seoul, Korea.

I. I NTRODUCTION High Speed Downlink Packet Access (HSDPA) is introduced to increase WCDMA[1] downlink packet data throughput in the Release 5 of the 3GPP UTRAN specifications. HSDPA offers theoretical peak data rates of up to 14.4 Mbps, which is achieved by implementing a fast and complex channel control mechanism based upon short physical layer frames (2 ms), Adaptive Modulation and Coding (AMC), fast Hybrid-ARQ and fast scheduling [2]. Fairness issues in scheduling have been studied in depth in [3], [4]. The proportionalf air (PF) algorithm, most popular packet scheduling algorithm considering fairness, was thoroughly investigated in [5], [6], [7]. Three packet scheduling algorithms namely Max CIR, Proportional Fairness (PF), and Round Robin (RR), are compared in [8] focusing on the achievable throughput of each user in HSDPA. Some alternative approaches include scheduling schemes that consider inter-cell transmission [9] and multi-user transmission in one slot [10]. Reference [11] proposes QoS based scheduling algorithms for real-time data users over shared wireless link. [12] proposes an algorithm that provides QoS guarantees using barrier functions. A quality based admission control algorithm is derived in [13]. The interaction between admission control and fast scheduling have been unexplored under mixed

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service requirements in HSDPA networks, although some work has been done in this area for UMTS networks [14], [15] that use dedicated channels unlike HSDPA. None of the existing works provide policy driven QoS guarantee either. For example, a service operator may have a certain policy on how to prioritize QoS classes during times of overload while another policy may determine how to distribute surplus capacity when the total guaranteed bit rates do not exceed the capacity. Another service provider, may have a different allocation policy during times of overload and may choose to improve channel quality by increasing effective code rate when there is surplus capacity. In this paper we consider such policy based QoS support, and show that our SPS algorithm very effectively satisfies users by guaranteeing such QoS requirements, in cooperation with the admission control mechanism at RNC. II. HSDPA S YSTEM Figure 1 sketches the hierarchical structure of an HSDPA network. In a typical HSDPA network, data enters the HSDPA/UMTS core network directly from the Internet or from the PSTN through a Packet Data Switching Node(PDSN). In the core network data is routed through the GGSN and SGSN, and into the RNC of the radio access network (RAN). It is then forwarded to the Node-B (base station) and finally to the mobile station over the radio link. PSTN/PDSN

Core Network

GGSN

SGSN

RNC Node B

Internet

for high speed data. A new downlink transport channel HS-DSCH (High Speed Downlink Shared Channel) was introduced, that carries data to the selected UE (or UEs) during each transmission time interval (TTI) of 2 ms. The transported bits from HS-DSCHs are mapped onto up to 15 physical downlink shared channels (HS-PDSCH) each using a separate orthogonal cdma code with a spreading factor of 16. The associated High Speed Shared Control Channel (HS-SCCH) is used to communicate control information between the UE and NodeB. B. Adaptive Modulation and Coding In the uplink direction, HS-SCCH channels are used by the UEs to notify the Node-B of the Channel Quality Indicator (CQI) and a positive or negative acknowledgement pertaining to the received frame. CQI indicates the instantaneous channel quality experienced by the user, so that the Node-B can adjust its transmission parameters (modulation type, coding rate, number of codes) to cope with variations in channel conditions. The CQI reported by the UE corresponds to transmission parameters (modulation type, coding rate, number of codes) that would result in the maximum data rate possible while providing an acceptable block error rate (BLER) for the current link conditions. The reported CQI value is then used by Node-B to determine the appropriate parameters or modulation and coding set (MCS) for the next packet transmission to the UE. The actual parameters used are notified to the UE using the downlink HSSCCH channel.Several AMC schemes are proposed including QPSK and 16QAM with coding rates of 1/3, 1/2 and 3/4. In order to reduce the latency involved in link adaptation the scheduling functionality has been moved from RNC to Node-B.

HSDPA

C. UE Categories Fig. 1.

HSDPA Network Architecture

A. Newly added channels Instead of dedicated channels as in release 99, HSDPA uses shared wireless downlink channels

The UEs are divided into 12 different categories based on their capabilities. For example, UE category k for k = 1 or 2 can only support data rates upto 1.2 Mbps using 5 simultaneous physical channels (codes) and has minimum inter TTI interval min T T I(k) of 3. If user ui from category k is scheduled to transmit in T T I t, the earliest time ui

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can be scheduled next is t+min T T I(k). Category 7 can theoretically (under perfect link conditions) support upto 7.21 Mbps using 10 codes and has minimum inter TTI interval of 1.

Carrier transmission power Maximum Power Carrier transmit power Non-HSDPA power HS-DSCH required power

RNC

GBR

Node B

CQI report

UE

SPI

NonHSDPA power

D. Hybrid Automatic Repeat Request Pilot Power Measurement

Hybrid automatic repeat request (HARQ) is a technique where UE stores previous transmissions that are in error in soft memory to be combined with future re-transmissions for decoding. For each packet the UE sends HARQ feedback (ACK or NACK) to inform the Node-B whether a retransmission is required or not. HARQ uses one of two different schemes, with identical retransmissions, often referred in the literature as Chase combining, or with non-identical retransmissions, otherwise called incremental redundancy. E. Admission Control and Scheduling Admission control is done at the RNC as in release ’99, while scheduling of admitted users is done by MAC-hs scheduler at the Node-B. Resource allocation, admission control and scheduling are collaborative efforts between the RNC and the Node-B. The Node-B receives guaranteed bit rate (GBR) and scheduling priority indicator (SPI) values from the RNC, which it can use to make scheduling decisions. On the other hand RNC allocates channelization codes and power for HSDSCH and HS-SCCH transmissions based on load and performance measurements provided by NodeB. These measurements include but are not limited to the total carrier power, non-hsdpa power and the HS-DSCH required power. HS-DSCH required power is reported per SPI and is an estimate of the total power needed to serve each admitted user with that SPI at their GBR. The RNC also receives an Ec /N0 measurement of the CPICH channel from the new user seeking admission. Based on all these reports the RNC can estimate whether the user can be granted access without deteriorating the services to the existing users. III. Q UALITY BASED HSDPA A DMISSION C ONTROL We use a quality based HSDPA admission control algorithm that was proposed in [13] with some

HSDPA

Non-real time R99 Real time R99 Common channels

(a) Exchange of parameters and measurement reports Fig. 2.

Total Carrier Power

(b) Power budget

Admission control parameters

modifications. In this approach a new user is admitted only if it can be served with its target bit rate without degrading the throughput of all the users with the same or higher SPI (priority) from their target bit rates. First the average HS-DSCH power allocated to user k is estimated as Mk 1 X Pk = Pk0 (m), (1) N m=1

Pk0 (m)

where is the allocated transmission power in the m-th TTI where the user was scheduled, and Mk is the number of TTIs user k was scheduled out of the N TTIs. When code multiplexing is used, we proportionally adjust Pk0 (m) according to the multicodes assigned to user k during that TTI. The average bit rate provided to user k over N TTIs is Rk =

Mk X 1 Bk (m)Ak (m) N · Ttti

(2)

m=1

Here Bk (m) is the transport block size (TBS) of the m-th transmission to the user. Notice that it is not the actual PDU size that goes into the transport block. If the user does not have enough data to send then much of the transport block could be empty and the user will be experiencing a much less avg bit rate than the provided bit rate. Ak (m) = 1 if an ack was received from the user and 0 otherwise. Given equations 1 and 2 the required power to provide all the users, that have SPI value x, with their GBR can be approximated as X GBRk PSP I (x) = Pk (3) Rk k∈SP I(x)

where GBRk is the GBR for user k, and SP I(x) is the set of users with SPI value x.

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Now let the target bit rate and priority of the new user be denoted GBRnew and SP Inew . Let PHSDP A , Pnew , and PSCCH be the allocated HSDPA transmission power, the estimated power required to serve the new user and the estimated power required for transmitting HS-SCCH respectively. Then the new HSDPA user is admitted only if X PHSDP A ≥ Pnew + PSP I (x)+PSCCH +P0 , x≥SP Inew

Here Po is a configuration parameter which represents a safety power offset to compensate for potential estimation errors. In [13] the required power to serve the new user at the target bit rate GBRnew is estimated as GBRnew Pnew = PT x,DSCH , (4) f (ρ) where ρ is the average experienced HS-DSCH SINR at the new user as estimated at the RNC from the pilot channel measurement report, and f (p) is the average throughput that a user can be served with when it is scheduled in every TTI with all the available transmission power. The function f (·) is assumed to be stored in a table in the RNC. However since we consider code multiplexing we use a slightly different equation to compute Pnew . Suppose the total number of channelization codes allocated by the RNC is given by ψ . Let CQIρ be the CQI value that the UE would report when experiencing an SINR of ρ. Let φρ be the number of multicodes corresponding to the transmission configuration (MCS) used by the Node-B when sending to the UE using CQIρ . Then the total transmission power usedto  send to the UE can be φρ estimated as PT x,DSCH ψ , and thus we have    φρ GBRnew Pnew = PT x,DSCH . (5) f (ρ) ψ IV. S CHEDULING USING S TRICT C HANNEL A LLOCATION P OLICIES The PF scheduler orders the receivers using the ri (t) metric th where ri (t) is the instantaneous data i (t) rate and thi (t) is the current throughput. However PF does not make any QoS guarantees. It considers all users to be equally important and adds a fairness property with respect to user throughput. We try

to incorporate both QoS constraints and throughput maximization in a strict set of policy requirements. Suppose a service provider differentiates its users using Scheduling Priority Indicator (SP I) values, where SP I ∈ C = {1.., 15}[2]. In general we assume higher classes (with higher SPI) have higher GBR values. Although the problem can be generalized for any number of SP I values, for simplicity let us consider only SP I values 1 and 2 with corresponding GBR values GBRs and GBRg . We will call these two classes Silver and Gold classes respectively. Let DR(cqii (t)) denote the maximum achievable instantaneous data rate indicated by the CQI for user i at TTI t, where DR(cqii (t)) ∈ {r1 , r2 , · · · , rk } such that r1 = rmin < r2 < · · · < rk = rmax . We assume that a user belonging to a particular class is on average under good enough channel conditions to be able to receive its GBR. Under this assumption, the goal of our policies is to define fair rules for governing resource allocation under all circumstances, i.e. to guarantee each user its GBR and fairly distribute the surplus capacity when there is enough resources, and to satisfy users from higher classes before the lower classes when there is not enough resources. Although it is the admission control algorithm’s job to make sure that all admitted users can be satisfied, situations could arise due to user mobility when such guarantees cannot be made. Our policies are as follows: (P1) A silver user can be scheduled only if all gold users have been satisfied. (P2) If there are multiple gold users with throughput less than GBRg , the gold user ui with the highest value of DR(cqii (t)) is scheduled. (P3) A silver user s with throughput ths (t) less than GBRs has higher priority than any gold or silver user that meets its GBR. (P4) If there are multiple silver users with throughput less than GBRs while all gold users have been satisfied, a silver user ui with the highest value of DR(cqii (t)) is scheduled. (P5) When all users have met their GBR, surplus capacity must be proportionally distributed

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among the gold and silver users under similar conditions according to their GBRs. V. M ARGINAL U TILITY F UNCTION Let N be the set of users in the system who can receive at T T I t. We will define marginal utility functions Mc (thi (t)) for each class c ∈ {Gold, Silver}, whose purpose is to assign a utility value, following the policy rules described earlier, to each user i ∈ N at T T I t according to its class c, current data rate di (t) and current throughput thi (t). Eventually the utility values will be used to determine which user(s) will be scheduled at t. Let Mc (thi (t)) = Pc (thi (t)) · di (t) where Pc denotes the preliminary utility function which we define shortly. Then for any gold user g and silver user s, functions PGold and PSilver have to follow the following conditions: (C1) PGold (thg (t))rmin > PSilver (ths (t))rmax , for 0 ≤ thg (t) < GBRg and 0 ≤ ths (t) ≤ rmax . (C2) PSilver (ths (t))rmin > PGold (thg (t))rmax , for 0 ≤ ths (t) < GBRs and GBRg ≤ thg (t) ≤ rmax . g (C3) PSilver (ths (t)) = PGold ( GBR GBRs · ths (t)), for GBRs ≤ ths (t) ≤ rmax and GBRg ≤ thg (t) ≤ rmax .

user. ( αβ + 1 PSilver (x) = rmax − PGold (x) =

(

GBRg GBRs x

if 0 ≤ x < GBRs if GBRs ≤ x ≤ rmax

α2 β + α + 1 if 0 ≤ x < GBRg rmax − x if GBRg ≤ x ≤ rmax

Functions PGold and PSilver are shown in Fig. 3. Notice that maximum PSilver value for a silver user s with throughput ths (t) ≥ GBRs and maximum PGold value a gold user g with throughput thg (t) ≥ GBRg , is β . So the maximum marginal utility (Mc ) for these users is βrmax . The minimum marginal utility for a silver user s0 with ths (t) < GBRs is (αβ + 1)rmin > βrmax . This satisfies conditions (C2) and (C4). Similarly if ths (t) < GBRs , MSilver (ths (t)) ≤ (αβ + 1)rmax . For a gold user with thg (t) < GBRg , MGold (thg (t)) ≥ (α2 β + α + 1)rmin > (αβ + 1)rmax . This satisfies conditions (C1) and (C5). It can also be noticed from the figure that when all users meet their GBR, condition C3 is also satisfied. Also since two gold users with throughtput less than GBRg has the same P value, the one with the higher data rate will have a higher marginal utility, which conforms to (P2). Conformance to (P4) can be shown using similar reasoning.

(C4) For any two silver users s and s0 , PSilver (ths0 (t))rmin > PSilver (ths (t))rmax , if 0 ≤ ths0 (t) < GBRs and GBRs ≤ ths (t) ≤ rmax . (C5) For any two gold users g and g0 , PGold (thg0 (t))rmin > PGold (thg (t))rmax , if 0 ≤ thg0 (t) < GBRg and GBRg ≤ thg (t) ≤ rmax . Note that Condition (C1) and (C5) corresponds to policy (P1), (C2) and (C4) corresponds to (P3), and Condition (C3) corresponds to (P5). We define functions PGold and PSilver satisfying the conditions above as follows. Let β = rmax − GBRg , α = rrmax and x be the throughput of the min

Fig. 3.

PGold and PSilver

Suppose there are more than two classes, i.e. |C| > 2. Let GBRmax denote the GBR associated to the highest class or SPI. Then Pc can be

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A. OPNET Simulator generalized for any SP I value c ∈ C as follows: ( αc β + αc−1 + · · · + α0 , if 0 ≤ x < GBRc A quality based access control algorithm is imPc (x) = plemented at the RNC as described in section III. max rmax − GBR GBRc x, if GBRc ≤ x ≤ rmax At each TTI Node-B schedules one or more users from the scheduling candidate set (SCS) to receive A. Strict Policy Scheduling Algorithm packets based on the scheduling algorithm being In HSDPA the UEs are divided into 12 different used. SCS includes (i) users with more than N categories based on their receiver and transmitter = 6 packets waiting in the transmission queue in capabilities. If user ui from category k is sched- the Node-B, (ii) users with a head-of-line (HOL) uled to transmit in T T I t, the earliest time ui PDU delay larger than THOL = 100 ms, and (iii) can be scheduled next is t + min T T I(k), where users with pending packets in the retransmission min T T I(k) is the minimum inter TTI interval queues. Retransmission packets have higher priority for category k. For example, UE category 1 can over first time transmissions. An MS measures the only support data rates upto 1.2 Mbps using 5 SINR for each received packet and reports the HS-PDSCH codes and has a min T T I(k) of 3. corresponding CQI back to the NodeB. For this, Suppose U is the list of users that are elligible to actual value interface (AVI) [16] is used to map receive in TTI t. A user is elligible if there are a given modulation and coding set (MCS) to a packets to be sent to that user and min T T I(k) received per-packet average SINR for obtaining a for that user has elapsed since its last reception. specific BLER (we use 0.1). For each UE category Let M be the number of codes allocated for the we use a separate AVI table that maps an MCS HS-DSCH channels and codes lef t be the number to a corresponding threshold SINR value. A UE of codes left to be assigned. During each TTI t the reports the maximum possible CQI for its current following steps are used to produce the list of users channel condition once every 10 TTIs. Error decision for a received packet is also made based on that are scheduled to receive data. the threshold SINR for the MCS associated to the 1. let i be the user such that i = transmitted packet. If the received SINR is less than argmax{Mcj (thj (t))} where user j belongs the threshold SINR the packet is in error, otherwise j to class cj . Let cqii be its requested CQI , a uniformly distributed random number y ∈ [0; 1] codes(cqii ) be the number of codes required. is generated. If y ≥ 0.1 the packet is successfully received. We also model a delay of 12 ms for the (i) if (codes(cqii ) < codes lef t) send to user i using data rate DR(cqii ) Node-B to get the associated ACK/NACK response back, from the time of transmission. We assume else Chase combining for the H-ARQ process and use send to user i at the maximum rate possible using codes lef t number of the following model[17]: codes.    n  X Es Es (ii) update codes lef t and remove i from U . n−1 = · (6) N0 C,n N0 k 2. if (codes lef t > 0 and U 6= φ) goto Step 1. k=1 VI. S IMULATIONS We developed an HSDPA system by extending the UMTS system in the OPNET simulator. Our system extensively simulates all the key entities of the network such as UEs, Node-B, RNC, SGSN etc. with most of the functionalities at all the protocol layers. In the following section we briefly describe the relevant portions of our simulator implementation.

where (Es /N0 )C,n represents the combined Es /N0 after n transmissions and (Es /N0 )k corresponds to the kth transmission.  is the Chase combining efficiency which is set to 0.93. In Chase combining an identical version of the original frame has to be retransmitted. Therefore when multi-user physical layer frames (code-multiplexing) are used, even the users that received their packet correctly during the original transmission will receive the retransmission.

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B. Traffic Model and Performance Metrics

0.9

Cumulative Distribution

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.2

0.25

Fig. 4.

Setting 10 W 10 Chase Combining 6 4 Every 10 TTI 7 1-Rx Rake Vehicular Outdoor 10 DB 2km 0 - 75 mph 1000 TTI

C. Performance Results We ran a series of simulations with the quality based admission control algorithm applied at the RNC. We compared our SPS algorithm with the Proportional Fair (PF) algorithm. We use two different versions of PF, one using code multiplexing and the other without. We will call the PF

0.35

0.4

0.45

0.5

Cumulative Distribution for Pnew

SPS Throughtput

PF_CM Throughput

PF throughput

3.5 3 2.5 2 1.5 1 0.5 0 -10

-8

-6

-5

-4

-3

Power offset (Po) [dB]

TABLE I MAIN SIMULATION PARAMETERS Parameter Total HS-PDSCH power Number of HS-PDSCH codes H-ARQ Number of H-ARQ channels Max number L1 transmissions CQI reporting interval HSDPA terminal category User receiver type Path loss model Shadow fading std. Site-to-site distance User speed Throughput window

0.3

Pnew [watts]

HS-DSCH Throughtput (bps)

We have a total of 30 HSDPA receivers with streaming services that are arbitrarily placed in the network. Half of the users belong to the silver class and the other half to gold. The GBR for the two classes are 128 kbps and 256 kbps respectively. All users belong to category 7. The offered traffic for each user is equal to their corresponding GBR. For a single simulation streaming calls are generated according to a random uniform process during the first 25 seconds and the length of each simulation is 50 seconds. Each user has a playout buffer that stores incoming packets. During the initial buffering the user waits till the amount of data in the playout buffer reaches the amount that can be played out in 5 seconds, i.e. a silver user waits till it buffered data reaches 640 kbits and for a gold user the amount is 1280 kbits. A user is labeled unsatisfied if the initial buffering time for that user takes more than 8 seconds or anytime during playout the buffer runs out of data to play. We do not drop any user during the simulation once it is admitted. The main parameter settings of our simulations are shown in Table I.

1.0

Fig. 5.

Average HS-DSCH cell throughput

algorithm with code multiplexing PF CM. Fig. 5 compares the throughputs for the three algorithms varying the safety power offset parameter Po where Po ∈ {1.0, 1.6, 2.5, 3.15, 4.0, 5.0}. In fig. 5 the Po is expressed in decibels relative to the total HSPo DSCH power, i.e. Po [dB] = 10log10 ( PHSDP ). The A cumulative distribution function of the estimated additional power (Pnew ) needed for the new users requesting access is shown in Fig. 4. It can be seen that around half of the users need 0.2W 0.35W and the other half need 0.35W - 0.50W. SPS produces around 65% more throughput than PF by taking advantage of code multiplexing. PF CM has comparable performance to SPS in this regard as it is using code multiplexing also. Since we do not drop any user once they are admitted, the throughput remains similar for all values of Po . For higher values of Po a smaller number of users are admitted at any given time; however the users

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SPS (spi=2) PF (spi=2) PF_CM (spi =2 )

1

SPS (all users) PF (all users) PF_CM (all users)

SPS

Number of satisfied users (SPI 1)

Unsatisfied user probability

PF_CM

12

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

10 8 6 4 2 0

0 -10

-8

-6

-5

-4

-3

-10

Fig. 6.

Unsatisfied user probability

SPS

PF_CM

-8

-6

-5

-4

-3

Power offset (Po)[dB]

Power Offset (Po)[dB]

Fig. 8.

PF

Number of satisfied users with spi 1

consequently decreasing the number of satisfied users as well.

25

Number of total satisfied users

PF

14

20

15

VII. C ONCLUSION

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We have investigated the performance of our QoS aware strict policy scheduling algorithm (SPS) in HSDPA systems when used in conjunction with a quality based access control algorithm. We compared our algorithm against two versions of Propotional Fairness schedulers using the HSDPA simulator that we developed in OPNET. Our results show SPS performs significantly better in terms of reducing unsatisfied user probability, while increasing the number of satisfied users and system throughput at the same time.

5

0 -10

-8

-6

-5

-4

-3

Power offset (Po)[dB]

Fig. 7.

Number of total satisfied users

with a lower SPI that were already admitted before the higher SPI users, stay on and keep using up resources. This keeps the throughput at a high level at all times. Fig. 6 shows the ratio of unsatisfied users to the total number of users admitted. Fig. 7 and 8 give the number of total satisfied users and satisfied gold users respectively. SPS can significantly reduce the number of unsatisfied user probability while increasing the number of satisfied users for all values of Po . For Po = 1.0 watt, only 22% of the users are unsatisfied when SPS is used, while for PF and PF CM this number grows to 88% and 70% respectively. For PF and PF CM the increase in the number of satisfied users as Po increases is due to the reduction in contention for resources as the number of admitted users is decreased. On the other hand since SPS strictly follows the admission control algorithm’s intent, when P0 is increased fewer users are admitted,

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[7] T. Kolding, “Link and system performance aspects of proportional fair scheduling in wcdma/hsdpa,” in Vehicular Technology Conference, 2003. VTC 2003-Fall. 2003 IEEE 58th, vol. 3, pp. 1717– 1722. [8] Y. Ofuji, A. Morimoto, S. Abeta, and M. Sawahashi, “Comparison of packet scheduling algorithms focusing on user throughput in high speed downlink packet access,” The 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 3, pp. 1462– 1466, 2002. [9] T. Bonald, S. C. Borst, and A. Prouti‘ere, “Inter-cell scheduling in wireless data networks,” in Proc. European Wireless Conference 2005. [10] F. Berggren and R. Jantti, “Multiuser scheduling over rayleigh fading channels,” in Proc. IEEE Globecom, December 2003. [11] M. Andrews, K. Kumaran, K. Ramanan, A. Stolyar, P. Whiting, and R. Vijayakumar, “Providing quality of service over a shared wireless link,” Communications Magazine, IEEE, 2005., vol. 39, no. 2, pp. 150–154, Feb. 2001. [12] P. Hosein, “Qos control for wcdma high speed packet data,” in 4th International Workshop on Mobile and Wireless Communications Network. [13] K. Pedersen, “Quality based hsdpa access algorithms,” in Vehicular Technology Conference, 2005, pp. 2498– 2502. [14] S. Elayoubi, T. Chahed, and G. Hbuterne, “Resource management in umts: Admission control and packet scheduling,” in ICON 2003, October 2003. [15] S. Pal, M. Chatterjee, and S. K. Das, “Call admission control and scheduling policies for umts traffic for qos provisioning,” in High Speed Networks and Multimedia Communications 7th IEEE International Conference, HSNMC 2004, 2004. [16] S. Hmlinen, P. Slanina, M. Hartman, A. L¨ appetelinen, H. Holma, and O. Salonaho, “A novel interface between link and system level simulations,” in ACTS Mobile Telecommun, Oct. 1997, pp. 599–604. [17] F. Frederiksen and T. Kolding, “Performance and modeling of wcdma/hsdpa transmission/h-arq schemes,” in Vehicular Technology Conference, 2002, pp. 472– 476.

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