DGS-PQ Method - HSDPA Basic Principles - Flate-Rate Packet Scheduling for the WCDMA Systems

CHAPTER 4 Flate-Rate Packet Scheduling for the WCDMA Systems

4.2 HSDPA Basic Principles

4.3.4 DGS-PQ Method

Fig. 4.8: A peudocode for DDT-PQ scheme

4.3.4 DGS-PQ Method

To maximize the operator’s revenue, a Node-B can reserve some capacities of the PQ for CPs only when the network load is high. That means the CPs have more chance to be served than FRPs when the system load is heavy. Let Guard Slots (GS) denote the number of the reserved capacities of the PQ for the CPs. The concept of GS is similar to that of guard channel used in cellular network [39-42]. In addition, a Node-B can dynamically adjust the value of GS, i.e., increase or decrease, for CPs depending on the traffic load. In our design, the value of GS can have a fraction part to represent the probability of new

FRPs request can be put into PQ. For example, if GS is set to be 1.2, then all new CPs request and 80% of new FRPs request will be allowed to be put into PQ whenever free capacity of PQ is 2. We name this control admission policy as GS admission procedure.

We refer this scheduling methd as Dynamic Guard Slots in a PQ for CPs (DGS-PQ).

The queueing model for DGS-PQ scheme is depicted in Fig. 4.9. The working scenario is same with P-PQ method except that an an adjustable portion of the PQ is reserved for the new downlink CPs. In this scheme, the GS values of the CPs have a Lower Bound (GSLB) and an Upper Bound (GSUB). A larger GS value increases the probability that a CP is served; a lower one decreases the probability. By adjusting the GS value based on the system load, we can control the dropped probability of CP in the PQ.

When the GSLB is chosen, a Node-B can not decrease the GS value for the CPs lower than it. That means the worse case of dropped probability of CP can be controlled. When the GSUB is chosen, a Node-B can not increase the GS value for the CPs higher than it.

That means the best case of dropped probability of CP can be controlled.

Fig. 4.9: A queueing model for DGS-PQ scheme

The proposed algorithm of dynamically adjusting GS implementation in Node-B can be described as follows. The DP of CP (P1) and FRP (P2) will also use in this method. When the

Priority order (CP_G, CP_P, FRP_G)

GS for (CP_G, CP_P)

Priority Queue (PQ) CP_Gs

CP_Ps

FRP_Gs

d. CP_G, FRP_G, or CP_P is rejected

GS admission procedure Accept

e. Start to transmit

HS-SCCH

HS-DSCH

...

f. Transmission completes a. new CP_G request

b. new FRP_G request c. new CP_P request

Priority order (CP_G, CP_P, FRP_G)

GS for (CP_G, CP_P)

Priority Queue (PQ) CP_Gs

CP_Ps

FRP_Gs

d. CP_G, FRP_G, or CP_P is rejected

GS admission procedure Accept

e. Start to transmit

HS-SCCH

HS-DSCH

...

f. Transmission completes a. new CP_G request

b. new FRP_G request c. new CP_P request

DP of CP is larger than P1 and GS is lower than GSUB, then GS can be increased by GSSV.

Otherwise, when the DP of FRP is larger than P2 and GS is higher than GSLB, then GS can be decreased by Guard Slots Step Value (GSSV). For implementation consideration, a lower P1 or a higher GSUB value can gurantee the throughput for CPs; on the other hand, a lower P2 or a lower GSLB value can gurantee the fairness for FRP. The effects of dynamically adjusting the GS can gurantee the system throughput of CP even when the FRP traffic is heavy, and can gurantee the fairness for FRPs. The values of the P1,P2,GSSV,GSLB,GSUB and GS value can be chosen by mobile operators. The peudocode of the proposed algorithm is described in Fig.

4.10.

--- Parameters:

GS : Guard Slots of PQ for new CP arrives

SW (Slicing Window) : a piece of system processing time PQR: free capacity of PQ

P1: the acceptable Dropped Probability (DP) of CP P2: the acceptable Dropped Probability (DP) of FRP GSLB: Guard Slots Lower Bound

GSUB: Guard Slots Upper Bound

GSSV: Step Value of Guard Slots in a PQ

Pseudocode

Initialize assign GS value and renew a timer for current SW

Repeat

(1) Any new downlink CP and FRP do not need to be put into PQ goto 3) (2) GS Admission procedure

(a) if [PQR> =( +1) ], PQ accepts CP and FRP





else if (PQR <= ), PQ rejects CP and FRP else if (PQR = )

PQ accepts CP and ( - GS)*100% FRPs in current SW

(b) PQR - =1 if accept CP or FRP (3) If current SW !=0 goto (5)

(a) Recalculate the DP of CP and DP of FRP based on the numer of CPs and FRPs which accept or Discard in previous (n-1) SWs and current SW

(b) If DP of CP > P1 and GS < GSUB , GS + =GSSV , goto (d) (c) If DP of FRP > P2 and GS > GSLB , GS - =GSSV d) Renew a SW timer , goto (1)

4) Upadte the number of CPs and FRPs which accept or Discard in current SW 5) Update Current SW and goto (1)

End Repeat

--- Fig. 4.10: A peudocode for DGS-PQ scheme

4.4 Analytic Models

In our analysis, The notation of the size of PQ is B and the number of HS-SCCH in a cell for all schemes is C. The arrivals of CP_G, CP_P and FRP_G form Poisson processes with mean λ^cg_,_λ^cb_and λ^fg, respectively. The service time of CP_G, CP_P and FRP_G is

assumed to be exponentially distributed with mean ¹/µ^cg_,¹^/µ^cb_and¹^/µ^fg, respectively. We can use the M/M/C/B Markov process to model the M-PQ, P-PQ, DDT-PQ and DGS-PQ schemes, and they are described below.

4.4.1 M-PQ Method







^GS





^GS



For M-PQ scheme, let state (i,j,m,n) denote that there are in total i CP_Gs and FRP_Gs transmitting, and j CP_Ps transmitting, in total m CP_Gs and FRP_Gs waiting, and n CP_Ps waiting in the PQ. Part of the state transition diagram of M-PQ scheme is depicted in Fig. 4.11. Let Pⁱ^,^j^,^m^,ⁿdenote the steady-state probability of the network in state (i,j,m,n) and S^M be the set of existing states for this process. S^M can be expressed in (4.1).

(4.1)

Fig. 4.11: The state transition diagram of M-PQ scheme

From the balance equations which are complicated, not shown here, and the

constraint iterative algorithm [43]. The dropped probability of CPs (CP_Gs and CP_Ps) and FRPs

(P^cp^_^M and P^frp^_^M), the network utilization of CPs (CP_Gs and CP_Ps) (U^cp^_^M) can be expressed in (4.2)-(4.4), respectively.

i,j,m,n

For P-PQ scheme, let state (i,j,k,x,y,z) denote that there are in total i CP_Gs

transmitting, j FRP_Gs transmitting, and k CP_Ps transmitting, in total x CP_Gs waiting, y FRP_Gs waiting, and z CP_Ps waiting in the PQ. Part of the state transition diagram of P-PQ scheme is depicted in Fig. 4.12. Let Pⁱ^,^j^,^k^,^x^,^y^,^zdenote the steady-state probability of the network in state (i,j,k,x,y,z) and S^P be the set of existing states for this process. S^P can be expressed in (4.5).

(4.5)

Fig. 4.12: The state transition diagram of P-PQ scheme

From the balance equations which are complicated, not shown here, and the

constraint obtained by an iterative algorithm. The dropped probability of CPs (CP_Gs and CP_Ps) and FRP_Gs (P^cg^_^Pand P^frp^_^P), the network utilization of CPs (CP_Gs and CP_Ps) (U^cp^_^P) can be expressed in (4.6)-(4.8), respectively.

(4.6)

4.4.3 DDT-PQ Method

For DDT-PQ scheme, let state (i,j,k,x,y,z) denote that there are in total i CP_Gs transmitting, j FRP_Gs transmitting, and k CP_Ps transmitting, in total x CP_Gs waiting, y FRP_Gs waiting, and z CP_Ps waiting in the PQ. Part of the state transition diagram of DDT-PQ scheme is depicted in Fig. 4.13. The difference of the state transition diagram and that of P-PQ is that there are two extra dotted lines representing the operations of DT for FRP_Gs. For example, state (i,j,k,x,y,z) may change to state (i,j,k,x,y-1,z) if there is a FRP_G’s DT expires and the FRP_G is dropped from the PQ. The DT of FRP_G is assumed to be exponentially distributed with mean ¹/ µ^dt^{. Let} ^Pⁱ^,^j^,^k^,^x^,^y^,^zdenote the steady-state probability of the network in state (i,j,k,x,y,z) and S^DDT be the set of existing states for this process. S^DDT can be expressed in (4.9)

(4.9)

Fig. 4.13: The state transition diagram of DDT-PQ scheme

( ) ( )

From the balance equations which are complicated, not shown here, and the constraint

∑

iterative algorithm. The dropped probability of CPs (CP_Gs and CP_Ps) and FRP_Gs

(P^cp^_^DDTand P^frp^_^DDT), the network utilization of CPs (CP_Gs and CP_Ps) (U^cp^_^DDT) can be expressed in (4.10)-(4.12), respectively.

(4.10)

(4.11)

(4.12)

4.4.4 DGS-PQ Method

For DGS-PQ scheme, let state (i,j,k,x,y,z) denote that there are in total i CP_Gs transmitting, j FRP_Gs transmitting, and k CP_Ps transmitting, in total x CP_Gs waiting, y FRP_Gs waiting, and z CP_Ps waiting in the PQ. Part of the state transition diagram of DGS-PQ scheme is depicted in Fig. 4.14. The difference of the state transition diagram

( ) [ ]

and that of P-PQ is that there are two extra dotted lines representing the operations of GS for CP_Gs. For example, state (i,j,k,x,y,z) may not change to state (i,j,k,x,y+1,z) because the new FRP_G request can not be put into the PQ based on GS admission procedure even the PQ still has free capacity and should be dropped. Let Pⁱ^,^j^,^k^,^x^,^y^,^zdenote the

steady-state probability of the network in state (i,j,k,x,y,z) and S^DGS be the set of existing states for this process. S^DGS can be expressed in (4.13).

(4.13)

Fig. 4.14: The state transition diagram of DGS-PQ scheme

( ) ( )

From the balance equations which are complicated, not shown here, and the constraint

∑

iterative algorithm. The dropped probability of CPs (CP_Gs and CP_Ps) and FRP_Gs (P^cp^_^DGS and P^frp^_^DGS), the network utilization of CPs (CP_Gs and CP_Ps) (U^cp^_^DGS) can be expressed in (4.14)-(4.16), respectively.

(4.14)

In this chapter, we consider a mobile data operator’s revenue that consists of the

transmission fee of normal users and the monthly fee of flat-rate users. Instead of calculating the total revenue, we propose a cost function representing the revenue loss due to blocked CPs and due to the loss of flat-rate users. Since CPs are charged by the volume of packets

transmitted. In a fully utilized network, re-transmitting blocked CPs only leads to more CPs

( ) [ ∑ ]

blocked. Therefore, we assume that blocked CPs in a fully utilized network will not be re-transmitted, and thus represent revenue loss. The revenue loss of blocked CPs is

proportional to the blocking probabilities (

P

^CP^_^G and

P

^CP^_^P) and the traffic load of CPs (

ρ

^CP^_^G and

ρ

^CP^_^P ). The monthly revenue loss due to blocked CPs can be expressed in (4.17).

C

^CP

= ρ

^CP^_^G

⋅ P

^CP^_^G

+ ρ

^CP^_^P

⋅ P

^CP^_^P (4.17)

The revenue loss due to the loss of flat-rate users also depends on the blocking probability. Since flat-rate users are not charged by the volume of packet transmission, blocked FRPs do not result in direct revenue loss. However, when the blocking probability is above a departure threshold, β , flat-rate users may become discontent and start to switch to other operators. We assume that the number of flat-rate users lost per month is proportional to the discrepancy of the blocking probability (

P

^FRP^_^G) above β. The monthly revenue loss due to lost flat rate users can be expressed in (4.18), where α represents the cost weighting factor of flat-rate users.

( ) ( )

{

^α^⋅ ⁻^β ^>^β

=

^FRP^_^G ^FRP^_^G

FRP

P if , P

otherwise

C

₀, (4.18)

The total monthly loss (C) is C_CP plus C_FRP . And we assume the the traffic load of CPs (

ρ

^CP^_^G ^and

ρ

^CP^_^P^{) are}

ρ

. We obtain the cost function, as shown in (4.19).

( )

( ) ( ) ( )

{

^ρ^⋅ ⁺ ⁺^ρ^α^⋅^⋅ ⁺⁻^β ^>^β

= +

= C

_CP

C

_FRP ^P^CPP^_^G ^P^CPP^_^P _P_CPP^P^FRP_{_}^__G^G_P_CPP^,^if_{_}_P^P^FRP_,_otherwise^_^G

C

(4.19)

When the cost weighting factor of FRPs is less than that of CPs (α ^<ρ), the scheduler

should give priority to CPs without considering the FRP blocking probability. On the other hand, when α is larger than twice of ρ, the scheduler should give priority to CPs when the FRP blocking probability is below the departure threshold (β), but it should give priority to FRPs when FRP blocking probability is above β. Note that β should be chosen to reflect the beginning of user dissatisfaction as the blocking probability increases; its proper value may be obtained from the past operation data.

To minimize the cost function, a same iterative algorithm shall also be developed as shown in Fig. 3.5. Based on the stationary state probabilities, we can obtain the performance measures and the minimum value of the cost function.

4.6 Numreical Analysis 4.6.1 Case I :

<

In the analysis below, we assume the the number of HS-SCCH in a cell (C) is 4 and the size of the PQ (B) is 20. We compare four packet scheduling methods: M-PQ, P-PQ、 DDT-PQ and DGS-PQ schemes. The mean service time of a CP_G (¹/µ^cg) and a FRP_G

(¹/ µ^fg) are assumed to be 10 ms, the mean service time of a CP_P (¹/µ^cb) is assumed to be 20ms. The session arrival rate of CP_G (λ^cg) and CP_P (λ^cb) are fixed at 50 and 100 packets/second respectively, and that of FRP_G (λ^fg) varies in the range of 50-150 packets/second.

In case 1, we let the cost weighting factor of flat-rate users α = 2500 and β^ should be chosen to be 0.08 to reflect the level of user dissatisfaction. Note that ρ^is choosen to be 5000 in our experiments, i.e., the cost weighting factor of FRPs is less than that of CPs.

Extra parameters are needed to be determined in DDT-PQ scheme. P1 and P2 are set to be 2% and 3%, DTLB and DTUB are set between 0.2 and 0.6 seconds, initial DT and

DTSV value are set to be 0.4 seconds and 10ms. Extra parameters are also needed to be

assumed in DGS-PQ scheme. P1 and P2 are set to be 2% and 3% same with the DDT-PQ scheme, the size of GSLB and GSUB can be reserved for CPs are set between 1 and 3, initial GS and GSSV value are set to be 2 and 0.1.

Fig. 4.15 plots the mean dropped probabilities of CPs (i.e. CP_G and CP_P) for four schemes as the FRP arrival rates increases. With special treatment for FRPs in DDT-PQ and DGS-PQ, these two schemes are trying to keep the dropped probability of CPs is below P1 when the arrival rate of FRP is high. The effects of DDT-PQ and DGS-PQ schemes on the mean dropped probability of CPs are changed slowly when the FRP arrival rate is higher than 125 packets/second. This is because in DDT-PQ scheme there is a dynamic DT for every FRP to limit the waiting time for it in PQ and in DGS-PQ scheme there is a dynamic GS of PQ can be reserved for CPs to let them have more chance to be kept in PQ.

When the FRP arrival rate is 170 packets/second, the DT value reachs DTLB in DDT-PQ scheme. That means there is no more adjustment of DT for FRPs even though the dropped probability of CPs is higher than P1. The effect is that the dropped probability of CPs will be higher than P1 when the FRP arrival rate is higher than 170 packets/second.

This indicates that DTLB in DDT-PQ scheme can also be dynamically adjust in system implementation consideration. When the FRP arrival rate is 170 packets/second, the GS value does not reach GSUB in DGS-PQ scheme. That means the adjustment of GS for CPs can still control the dropped probability of CPs higher than P1. According to the results, DDT-PQ and DGS-PQ schemes can have lower dropped probability of CPs comparing with two other schemes.

Average Drop Probability (CP)

50 60 70 80 90 100

110 120

130 140

150 160

170 FRPs arrival rate (packets/second)

Pcp_M

Pcp_P

Pcp_DDT

Pcp_DGS

Fig. 4.15: The average dropped probability of CP for four packet scheduling methods

Fig.4.16 plots the mean dropped probabilities of FRPs (i.e. FRP_G) for four schemes as the FRP arrival rates increases. With the special treatment for FRPs in DDT-PQ and DGS-PQ, these two schemes will have higher blocking probabilities for FRUSs. The cost becomes more significant as the traffic of FRPs increases. However, in these two

DDT-PQ and DGS-PQ schemes, they are also trying to keep the dropped probability of FRPs is below P2 when the FRP arrival rate is between 100 and 105 packets/second. But after the FRP arrival rate icreases more, trying to keep the dropped probability of CPs below P1 is important than trying to keep the dropped probability of FRPs below P2.

Average Drop Probability (FRP)

10%

12%

14%

16%

18%

20%

50 60 70 80 90 100

110 120

130 140

150 160

170 FRPs arrival rate (packets/second)

Pfrp_M

Pfrp_P

Pfrp_DDT

Pfrp_DGS

Fig. 4.16: The average dropped probability of FRP for four packet scheduling methods

Fig. 4.17 plots the mean network utilization of CPs (i.e. CP_G and CP_P) for four schemes as the FRP arrival rates increases. With the special treatment for FRPs in DDT-PQ and DGS-PQ, these two schemes are trying to let CPs to have more changes to be served even when the arrival rate of FRP is high . When the FRP arrival rate is 170 packets/second, the DT value reachs DTLB in DDT-PQ scheme. The effect in DDT-PQ scheme is that the network utilization of CPs are almost the same and can be guranteed when the FRP arrival rate is between 125 and 165 packets/second. When the FRP arrival rate is 170 packets/second, the GS value does not reach GSUB in DGS-PQ scheme. The effect in DGS-PQ scheme is that the network utilization of CPs are almost the same and can be guranteed when the FRP arrival rate is between 125 and 170 packets/second.

Because we choose different simulation parameters assumptions (i.e., DTLB and GSUB), there is a little different result between these two methods. No matter what parameters we choose, the result can implicitly indicate that these two methods are very effective to gurantee the packet revenues for mobile operators.

Average Network Utilization (CP)

2.15 2.2 2.25 2.3 2.35 2.4 2.45 2.5 2.55

50 60 70 80 90 100

110 120

130 140

150 160

170 FRPs arrival rate (packets/second)

Ucp_M

Ucp_P

Ucp_DDT

Ucp_DGS

Fig. 4.17: The average network utilization of CP for four packet scheduling methods

Fig. 4.18 plots the result of dynamically adjusting the DT value in DDT-PQ scheme as the FRP arrival rates increases. We assume the initial DT value is 400ms and DTLB , DTUB values are 200ms, 600ms. When the FRP arrival rate is 100 packets/second, the

dropped probabilities of FRPs reachs P2, the DT needs to increase to keep the dropped probability of FRP below P2. When the FRP arrival rate is 105 packets/second, the DT reachs DTUB and no more adjustment of DT in DDT-PQ scheme. That means the dropped probabilities of FRPs is higher than P2. When the FRP arrival rate is 130 packets/second, the dropped probabilities of CPs reachs P1, the DT needs to decrease to keep the dropped probability of CP below P1. When the FRP arrival rate is 165 packets/second, the DT reachs DTLB and no more adjustment of DT in DDT-PQ scheme. That means the dropped probabilities of CPs is higher than P1. Different analytic parameters assumptions, i.e., P1, P2, DT, DTLB and DTUB values in DDT-PQ scheme could be a little different numerical results.

Dynamic Drop Timer (ms) for FRP

0 100 200 300 400 500 600 700

50 60 70 80 90 100

110 120

130 140

150 160

170 FRPs arrival rate (packets/second)

Drop Timer

Fig. 4.18: The results of dynamically adjusting the DT value in DDT-PQ scheme

Fig. 4.19 plots the results of dynamically adjusting the GS value in DGS-PQ

scheme as the FRP arrival rates increases. We assume the initial GS value is 2 and GSLB , GSUB values are 1, 3. When the FRP arrival rate is 100 packets/second, the dropped

probabilities of FRPs reachs P2, the GS needs to decrease to keep the dropped probability of FRP below P2. When the FRP arrival rate is 110 packets/second, the GS reachs GSLB and no more adjustment of GS in DGS-PQ scheme. That means the dropped probabilities of FRPs is higher than P2. When the FRP arrival rate is 130 packets/second, the dropped probabilities of CPs reachs P1, the GS needs to increase to keep the dropped probability of CP below P1. When the FRP arrival rate is 170 packets/second, the DT does not reach GSUB. That means the dropped probabilities of CPs is not higher than P1. Different analytic parameters assumptions, i.e., P1, P2, GS, GSLB and GSUB values in DGS-PQ scheme could be a little different numerical results.

Number of Guard Slot of Queue for CP

0 0.5 1 1.5 2 2.5 3 3.5

50 60 70 80 90 100

110 120

130 140

150 160

170 FRPs arrival rate (packets/second)

No. of GS

Fig. 4.19: The results of dynamically adjusting the GS value in DGS-PQ scheme

4.6.2 Case II :

>

In case 2, we let the cost weighting factor of flat-rate users α = 20000 and β^

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