Channel Allocation for GPRS
Phone Lin and Yi-Bing Lin, Senior Member, IEEE
Abstract—Based on the GSM radio architecture, general packet radio service (GPRS) provides users data connections with vari-able data rates and high bandwidth efficiency. In GPRS service, al-location of physical channels is flexible, i.e., multiple channels can be allocated to a user. In this paper, we propose four algorithms for the GPRS radio resource allocation: fixed resource allocation (FRA), dynamic resource allocation (DRA), fixed resource tion with queue capability (FRAQ), and dynamic resource alloca-tion with queue capability (DRAQ). We develop analytic and sim-ulation models to evaluate the performance for these resource al-location algorithms in terms of the acceptance rate of both GPRS packet data and GSM voice calls. Our study indicates that DRAQ (queuing for both new and handoff calls) outperforms other algo-rithms.
Index Terms—Dynamic resource allocation, fixed resource allo-cation, general packet radio service, wireless data.
Shape parameter of Gamma dis-tributed packet transmission times. Shape parameter of Gamma dis-tributed packet inter arrival times. Shape parameter of Gamma dis-tributed GSM voice user cell resi-dence times.
GSM voice user mobility rate. GPRS packet arrival rate to a cell (the new GSM voice call arrival rate to a cell).
Voice handoff call arrival rate to a cell.
Expected GPRS packet transmission time if one channel is used to serve the packet (the expected GSM voice call holding time).
GPRS packet traffic (the GSM voice traffic) to a cell.
Net new/handoff voice call arrival rate.
Mean channel occupancy time of a voice call.
Number of channels in a cell. Average number of channels for a served packet.
Manuscript received May 5, 2000; revised November 22, 2000. This work was sponsored in part by the MOE Program of Excellence Research under Con-tract 89-E-FA04-4, in part by CCL/ITRI under ConCon-tract 2-10B, in part by Far-Eastone, in part by NSC, and in part by the Lee and MTI Center for Networking Research, National Chiao Tung University.
The authors are with the Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. (e-mail: liny@csie.nctu.edu.tw).
Publisher Item Identifier S 0018-9545(01)03068-7.
Maximum number of channels used to serve a GPRS packet.
Number of idle channels in a cell,
where .
Dropping probability for the GPRS packet (the new call blocking proba-bility for the GSM voice call). Force-termination probability for the GSM voice call.
Probability that a GSM voice call is not completed (either blocked or forced to terminate).
Maximum number of voice call re-quests buffered in the queue. GPRS packet transmission time (the voice call holding time).
Residence time of an GSM voice user at a cell .
Variance of Gamma distributed packet transmission times.
Variance of Gamma distributed packet inter arrival times.
Variance of Gamma distributed GSM voice user cell residence times. Average waiting time for the ac-cepted voice call requests.
I. INTRODUCTION
G
eneral Packet Radio Service (GPRS) [6] is a new bearer service for mobile networks [such as Global System for Mobile Communications (GSM) [13] and IS-136 [8]], which greatly improves and simplifies the wireless access to packet data networks (e.g., the Internet). In this paper, we assume that the mobile network for GPRS is GSM. Compared with the pre-vious mobile data services (e.g., circuit-switched data [4] and short message service [2]), users of GPRS benefit from shorter access times and higher data rates.Fig. 1 illustrates the GPRS architecture based on the GSM network [7]. In a GSM network, a mobile station (MS) com-municates with a base station subsystem (BSS) through the air interface. The BSS is connected to the mobile switching center (MSC) for the mobile applications. The MSC communicates with the visitor location register (VLR) and home location reg-ister (HLR) to track the locations of MSs. The reader is re-ferred to [13] for GSM details. In the GPRS architecture, MS, BSS, VLR, and HLR in the GSM network are modified. For ex-ample, the HLR is enhanced to accommodate GPRS user infor-mation. Two GPRS support nodes (GSNs), a serving GPRS sup-port node (SGSN), and a gateway GPRS supsup-port node (GGSN)
Fig. 1. GPRS architecture.
are introduced in GPRS. The SGSN is responsible for deliv-ering packets to the MSs. The GGSN acts as a gateway between GPRS and the external data networks. Between different GSNs within the GPRS network, the GPRS tunneling protocol is used to tunnel user data and signaling message.
Based on the GSM architecture, the GPRS air interface [5] has been implemented for communication between the MS and BSS. The GPRS physical channel dedicated to packet data traffic is called a packet data channel (PDCH). Different packet data logical channels can camp on the same PDCH, which are packet data traffic channels (PDTCHs) used for data transfer, packet common control channels (PCCCHs) used to convey the GPRS common control signaling, and packet dedicated control channels (PDCCHs) used to convey the GPRS control signaling for a dedicated MS. Allocation of channels for GPRS is flexible where one to eight channels can be allocated to a user or one channel can be shared by several users.
Fig. 2 illustrates the message flow for the GPRS uplink packet transfer. The downlink packet transfer is similar and is not de-scribed. To initiate packet transfer, an MS negotiates with the network for the radio resource in the access and assignment phase via PCCCH and possibly PDCCH (see Step 1 in Fig. 2). After this phase, the MS starts to transmit data blocks to the net-work via PDTCH (see Step 2 in Fig. 2) according to the agreed resource assignment. If the MS requires more PDCHs, it can specify the request through an assigned uplink block (see Step 3 in Fig. 2). The network and the MS then exchange the PD-CCHs to reallocate the resources for uplink transmission (see Steps 4 and 5 in Fig. 2). The amount of PDCHs for the request will be recorded in the quality of service (QoS) profile of the user at the SGSN. When the MS completes the transmission, it indicates the last data block (see Step 7 in Fig. 2). The net-work then terminates the uplink transmission by returning the final block acknowledgment (see Step 8 in Fig. 2). Note that in resource assignment (Step 1) and resource reassignment (Step 4), there are two alternatives: fixed resource allocation and dy-namic resource allocation. In the fixed resource allocation, the requested amount of PDCHs is allocated for the packet request. The packet request is rejected if the BS does not have enough radio resources to accommodate the request. On the other hand, the network allocates partial resources in dynamic resource al-location.
Fig. 2. GPRS uplink packet transfer.
In this paper, we propose four resource allocation algorithms: fixed resource allocation (FRA), fixed resource allocation with queue capability (FRAQ), dynamic resource allocation (DRA), and dynamic resource allocation with queue capability (DRAQ) for scheduling of the packet data and voice calls. Then we propose analytic and simulation models to evaluate the perfor-mance for these algorithms. Our study indicates that dynamic allocation for packet transmission and waiting queue for voice calls may significantly improve the performance of the network.
II. RESOURCEALLOCATIONALGORITHMS FORGPRS PACKET
REQUESTS ANDGSM VOICECALLS
This section describes four resource allocation algorithms for GPRS packet requests and GSM voice calls. We assume that a GPRS data request specifies channels for transmission. Based on the negotiated QoS profile, a cell may allocate re-sources on one or several physical channels to support the GPRS traffic, as described in Section I. We assume that the packets are transmitted at rate at a single channel. Consequently, if channels are assigned to a GPRS data request, then this packet request will be delivered with rate . Suppose that there are free channels at a cell when a GPRS data request or a GSM voice call request arrives. Algorithms FRA and FRAQ allocate the exact number of channels requested by the GPRS data re-quests. On the other hand, algorithms DRA and DRAQ may al-locate partial resources. All four algorithms alal-locate one channel for a voice request. In FRA and DRA, if no channel is available, the voice request is rejected immediately. In FRAQ and DRAQ, on the other hand, the voice call requests can be buffered in a waiting queue if all channels at a cell are busy. The intuition behind FRAQ and DRAQ is that packet transmission times are typically short. Thus, with the buffer mechanism, a voice request can be served after a short waiting time (when GPRS completes
Fig. 3. The timing diagram.
a packet transmission) instead of being rejected immediately at its arrival. The four algorithms are described below.
Algorithm FRA For a data request of channels, the BS assigns channels to the GPRS packet re-quest if . Otherwise, the GPRS packet request is rejected.
Algorithm DRA For a data request of channels, DRA al-locates at most channels to the request. Depending on the current available radio resources, the network shall negotiate with the GPRS MS for the QoS profile at the be-ginning of GPRS data transfer. Specifically, if , then channels are allocated to the request. If , then channels are allocated to the request. If , then the request is rejected.
Algorithm FRAQ FRAQ handles GPRS data requests in the same way as FRA. For GSM voice call requests, FRAQ provides a queue to hold GSM voice call requests when all chan-nels are busy. These queued GSM requests are served immediately when idle chan-nels are available. FRAQ may selectively queue the new calls only, the handoff calls only, or both, and the corresponding mech-anisms are called FRAQ_N (for new calls only), FRAQ_H (for handoff calls only), and FRAQ_NH (for both new calls and handoff calls), respectively.
Algorithm DRAQ DRAQ assigns channels to a GPRS data request in the same way as DRA and as-signs channels to GSM voice call requests in the same way as FRAQ. Thus, there are also three DRAQ variations: DRAQ_N (for new calls only), DRAQ_H (for handoff calls only), and DRAQ_NH (for both new calls and handoff calls), respectively.
III. ANALYTICMODELS
Several analytic models for circuit-switched-type channel al-location of mobile networks are described in [1] and [9] and ref-erences therein. We propose analytic models to investigate the performance of algorithms FRA, DRA, and FRAQ and validate these models by simulation experiments. The output measures of these models are the dropping probability for the GPRS packets and the GSM voice call incompletion probability (i.e., the probability that a voice call is blocked or forced to ter-minate).
We assume that the GSM voice call arrivals and GPRS packet requests to a cell form Poisson streams with rates and , respectively. Let ( ) be the voice call holding time (GPRS packet transmission time), which is assumed to be exponentially distributed with the density function and the mean voice call holding time (packet transmission time)
( ).
In the GSM (GPRS) network, if an MS moves to another cell during the conversation, then the radio link to the old BS is dis-connected and a radio link to the new BS is required to continue the conversation. This process is called “handoff” [3]. If the new BS does not have any idle channel, the handoff call is “forced to terminate.” In the analytic models, we consider the mobility of voice users but ignore the effect of mobility (handoff) on the GPRS packet transmission. Our assumption is justified as follows. Although a GPRS session can be elapsed for a long period, the individual packet transmission times are short, and the handoff procedure can be initiated after the current packet transmission is completed. On the other hand, voice call holding times are long enough so that handoffs may occur during the conversation. Thus the handoff effects of voice calls must be considered.
A. Analytic Model for FRA
This section proposes an analytic model for algorithm FRA. We first describe the handoff traffic model for voice users. Then we use the Zachary–Kelly model [15], [10] together with an iterative algorithm to derive the voice blocking probability and data dropping probability.
Consider the timing diagram in Fig. 3. Let be the res-idence time of a GSM voice user at a cell (where ). We assume that are independent and identically distributed random variables with a general function
with mean 1 . Let
be the Laplace transform of the cell residence time distribution. In the GSM voice call channel assignment of FRA, the handoff calls and the new calls are not distinguishable. Thus the new call blocking probability and the handoff call force-termination probability are the same (i.e., ). Let be the voice handoff call arrival rate to a cell and be the voice call incompletion probability (i.e., the probability that a voice call is blocked as a new call attempt or forced to terminate as a connected call). From [12], can be expressed as
The GSM voice call traffic to a cell is
(2)
and is
(3) To derive the new call blocking probability for GSM voice calls and the dropping probability for the GPRS packets, we consider a stochastic process with state , where and represent the number of outstanding voice calls and GPRS packets at a cell, respectively. Suppose that there are channels at a cell. Since the network assigns channels to every GPRS packet request in FRA, the following constraints must be satisfied:
and
Thus the state space of the stochastic process is
and
According to the Zachary–Kelly model, the stationary prob-ability of the state can be computed as
(4)
where , is obtained from (2) and is
(5)
The second and third terms of the right-hand side in (4) are the weights contributed by the GSM voice call traffic and GPRS packet traffic, respectively. The normalized factor in (5) is
used to ensure that .
With the above stochastic process model, is computed as follows. When a GSM voice call arrives at a cell, it is blocked if
no free channel is available at the cell. That is, when the GSM voice call arrives. Thus
(6) Similarly, when a GPRS packet request arrives at a cell, it is dropped if the number of idle channels is smaller than (i.e., ). (See (7) at the bottom of the page.) With (1), (2), (3), (6), and (7), the following iterative algorithm
[12] computes , , and .
The Iterative Algorithm for FRA Step 1) Select an initial value for .
Step 2) .
Step 3) Compute and by using (2) and (4)–(7). Step 4) Compute by using (1).
Step 5) If then go to Step 2).
Otherwise, go to Step 6). Note that is a predefined threshold set to 10 .
Step 6) The values for , and converge. Compute by using (3).
In all cases considered in this paper, the above algorithm always converges. The simulation experiments indicate that the algo-rithm converges to the correct values (see Section III-D). B. Analytic Model for DRA
This section proposes an analytic model for DRA. To simplify our discussion, the cell residence time for a GSM voice user is assumed to be exponentially distributed with mean 1 and Laplace transform
(8) In the real world, the cell residence time distribution may not be exponential. By using exponential assumptions, our analytic model serves for two purposes. First, exponential distribution provides the mean value analysis, which indicates the perfor-mance trend of DRA. Second, the analytic model is used to val-idate the simulation model that we use to study the performance of DRA with a general cell residence time distribution.
Algorithm DRA is modeled by a -state
Markov process. In this process, a state
denotes that a cell is occupied by voice calls, GPRS packets (each allocated channels), GPRS packets (each allocated
channels), GPRS packets (each allocated channels), , and GPRS packets (each allocated one channel), respectively. For the illustration purpose, we consider in our discussion. In this Markov process, a state is
represented by , where and
. Based on DRA described in the previous section, it is clear that the state space for this Markov process is
and
Let be the steady-state probability for state . By
convention if state . For all legal
states , we have
Fig. 4 illustrates the state transition diagram for DRA. The tran-sitions of the Markov process are described as follows. If state , the following transitions should be consid-ered. Let be the net new/handoff voice call arrival rate to a cell. Let . Then 1 is the mean channel occupancy time of a voice call at a cell.
1) At state , if a new voice call or
handoff call arrives, the process moves from state to with rate . The process moves
from state to with rate for
a voice call completion (or when the voice user moves to another cell).
2) If a GPRS request arrives when the process is at state
where ,
then one channel is allocated. Define as
if and
otherwise.
(9)
Then the process moves from state to
with rate . The process moves from state
to with rate when the
trans-mission is completed for a GPRS data request utilizing one channel.
3) If a GPRS request arrives when the process is at state
, where ,
then two channels are allocated. Define as
if and
otherwise.
(10)
The process moves from state to with rate . The process moves from state
to with rate when the transmission is
completed for a GPRS data request occupying two chan-nels.
Fig. 4. The state transition diagram for DRA.
4) At state , where
, if a GPRS data request arrives, then three channels are allocated. Define as
if and
otherwise.
(11)
The process moves from state to with rate . The process moves from state
to with rate when the transmission is
completed for a GPRS data request with three channels.
The transitions between and ,
, , are similar to that
be-tween and , , ,
. The balance equations for the Markov process are expressed as
(12) where , , and are obtained from (9), (10), and (11), re-spectively, and if and otherwise if and otherwise if and otherwise if and otherwise
In (12), the state probability if state
. The new voice call blocking probability , handoff voice call force-termination probability for voice calls, and dropping probability for the GPRS packet are derived as follows. A new voice call is blocked, a handoff call is forced to terminate, or a packet request is dropped if no free channel is available when the request arrives. Let be the set of the states where no free channel is available. Then
and and , , and can be expressed as
(13)
By substituting (8) and (13) into (1), we obtain . The voice call incompletion probability can be obtained by using (3). The probabilities , , and can be computed by an iterative algorithm similar to the one described in Section III-A, where are computed by (12) and , , and are computed by (13).
C. Analytic Model for FRAQ
This section proposes an analytic model for FRAQ_N. As in Section III-B, we assume that the cell residence time for a GSM voice user is exponentially distributed. Algorithm FRAQ_N can be modeled by a two-dimensional Markov process. A state in this process is defined as , where is the number of voice calls (either being served on the channels or buffered in the queue) at the cell and is the number of packets being transmitted on the channels. Let denote the size of the finite queuing mechanism (i.e., at most requests can be buffered in the queue). Based on the description of FRAQ_N in the previous section, it is clear that the state space for this Markov process is
Let denote the steady-state probability for state ,
where if state . For all legal states
, . Fig. 5 illustrates
the transition diagram for FRAQ_N. The transitions of the process are described as follows. For state , if
states , , , , the
transitions between and , , ,
and are considered, respectively. Otherwise, for a
state , the transitions between state
and do not exist. We consider the following cases.
(a)
(b)
(c)
Fig. 5. The state transition diagram for FRAQ_N. (a) Case I:0 x + K <
C. (b) CaseII: x + K = C. (c) Case III: C < x + K C + Q.
Case 1) [Fig. 5(a)]. In this case, free
channels are available at the cell and no voice call requests are buffered in the queue. If a GPRS request arrives when the process is at state , then channels are allocated. The process moves from
state to with rate . For a GPRS
is completed at state , the process moves from
state to with rate .
If a GPRS request arrives at state and , then channels are allocated. Define as
if
otherwise.
The process moves from state to
with rate . At state , if the transmission for a -channel GPRS data request is completed, the process moves from state to with rate . At state , if a new or handoff voice call arrives, then one channel is allocated to the voice call. In this case, the process moves from state to with rate . At state , if a voice call is completed or the GSM voice user moves to another cell, the process moves from state
to with rate . At state , if
a voice call is completed or the voice user moves to another cell, the process moves from state
to with rate . The process moves
from state to with rate for a new
or handoff voice call arrival.
Case 2) [Fig. 5(b)]. In this case, no free chan-nels are available at the cell. If a new voice call re-quest arrives, it will be buffered in the queue. On the other hand, if a handoff call or packet request arrives, it will be dropped. Thus the process moves from state to with rate . At state , there are voice calls served on the channels and voice call requests buffered in the queue. A served voice call releases the channel with rate , and the voice user of a queued request leaves the cell with rate . Thus the
process moves from state to with
rate . At state
, if the transmission for a -channel GPRS data request is completed, the process moves from
state to with rate . The
transition between and and the tran-sition between and in this case are the same as that in Case 1).
Case 3) [Fig. 5(c)]. In this case,
no free channels are available at the cell.
voice calls are served and voice call requests are buffered in the queue. At state , a served voice call releases the channel with rate , and the voice user of a queued request leaves the cell with rate . The process moves from state to
with rate .
At state , if a new voice call request ar-rives, it is buffered in the queue. The process moves from state to with rate . When the transmission for a GPRS data request with chan-nels is completed at state , the process moves
from state to with rate . The
transition between and and the tran-sition between and are the same as that in Case 2).
From the above state transitions, we write the balance equations and compute the probability by using the same iterative algorithm described in Section III-B.
The new voice call blocking probability , the handoff voice call force-termination probability , and the dropping probability for the GPRS packet are derived as follows. A packet request is dropped if the number of free channels is smaller than . Let be
Then can be expressed as
(14)
Since FRAQ_N queues the new calls only, the new voice calls and the handoff voice calls are distinguishable, and . From [14], can be expressed as shown in (15) at the bottom of the next page.A handoff voice call is forced to terminate if no free channel is available when the handoff request arrives. Thus
can be expressed as
(16)
From (1), (8), (15), and (16), we can obtain . The voice call incompletion probability can be obtained from (3). The probabilities and can be computed by an iterative al-gorithm similar to the one in Section III-A.The analytic model for FRAQ_H is similar to the one for FRAQ_N except that the handoff calls can be buffered instead of the new calls. The de-tails are not presented.
D. Simulation Validation
The analytic models are validated by simulation experi-ments. Furthermore, algorithms such as FRAQ_NH, DRAQ_N, DRAQ_H, and DRAQ_NH are evaluated by simulation experiments without analytic modeling. In the simulation experiments, we consider a 6 6 wrapped mesh cell structure.
TABLE I
COMPARISON OF THE ANALYTIC AND THE
SIMULATIONRESULTS FORFRA ( = ; = 100 ; = 0:2 ;
C = 7; K = 3)
The model follows the discrete event simulation approach in [11]. Table I lists and values for both analytic and simulation models for FRA. The details of the parameter setup in this table will be described in the following section. In this table, the errors between simulation and analytic models are below 1% in most cases and are always less than 5%. The table indicates that the analytic results match closely with the simulation data. Similar results for DRA, FRAQ_N, and FRAQ_H are observed and are not presented.
IV. PERFORMANCEEVALUATION
This section investigates the performance of the resource al-location algorithms. In our study, the input parameters , , , and are normalized by . For example, if the expected GSM voice call holding time is min, then
means that the expected inter voice call arrival time for GSM at a cell is 3 min. We assume that there is one frequency carrier (or seven channels) per cell, i.e., . For the cases where , similar results are observed and are not presented. Our study indicates that for the GPRS data acceptance rate and the GSM voice call completion, DRAQ_NH outperforms other al-gorithms in most cases. This high acceptance rate is achieved by reasonably slowing down the packet transmission.
A. Performance of FRA
In this section, we use FRA to investigate the performance of GPRS data transmission and GSM voice call completion. Sim-ilar results are observed in other algorithms and are not pre-sented.
1) Performance of GPRS Data Transmission: Fig. 6 plots as a function of and , where . Fig. 6(a) and (b) shows the effects of packet sizes, where (small packet size) and 10 (large packet size). Fig. 6(a) and (c) shows the effects of voice arrival rates, where (small arrival rate) and 5 (large arrival rate). Fig. 6(a) and (d) shows the effects of GSM voice user mobility rates, where
(low mobility rate) and (high mobility rate). Since the packet transmission rate is , the traffic becomes bursty when increases (i.e., a data transmission occupies more radio channels with shorter transmission time). A general phenom-enon in Fig. 6 is that increases as increases. This phe-nomenon reflects the well-known result that the performance of
(a) (b)
(c) (d)
Fig. 6. Impact of GPRS data transmission for FRA (C = 7). (a) =
100 ; = ; = 0:2 . (b) = 10 ; = ; = 0:2 .
(c) = 100 ; = 5 ; = 0:2 . (d) = 100 ; =
; = 2 .
a system (packet dropping probability) becomes worse as the packet arrival becomes bursty since each packet requests more channels. We also observe an intuitive result that increases as increases.
2) The Base Case: Consider Fig. 6(a) where the packet size is small ( ). In this case, the offered load of GPRS packets is small for , and it is not likely that multiple GPRS packets will arrive and be processed at the same time. That is, the packets do not compete among themselves. Instead, they compete with voice requests. For a large , it is more dif-ficult for packets to compete channels with the voice requests. Thus increases as increases.
3) Effects of Packet Size: In Fig. 6(b), the average packet size is ten times of that in Fig. 6(a). In this case, the packet traffic is large and the arrival packets compete with each other as well as the voice requests for the radio channels. The figure indicates that the increase of is very significant in two cases: when increases from three to four and from six to seven. This phenomenon is described as follows.
1) When , the GPRS network may accommodate two or more packets simultaneously (because the total number of channels is ). When , the GPRS can at most accommodate one packet at a time. Thus, when increases from three to four, significantly increases.
2) When , a packet arrival is dropped if some radio channels are already occupied by voice requests or an-other packet. Since , the probability that the system is serving one voice request is high. On the other hand, the probability of serving more than one voice call is relative low. Thus significantly increases when increases from six to seven. This phenomenon is also ob-served in Fig. 6(a).
When increases from four to five, only insignificantly in-creases (for ) or even decreases (for ). In this case, the effect of short data transmission time (i.e., the data transmission time decreases by 20% when increases from four to five) has balanced against the effect that more channels are occupied to accommodate a packet arrival. This effect di-minishes as continues to increase.
4) Effects of Voice Call Arrival Rate: In Fig. 6(c), the voice traffic is five times that in Fig. 6(a). In this case, the voice traffic is large and the arrival packets become less competitive com-pared with the voice requests. The consequence is that the bursty data effect occurs when is smaller than that in Fig. 6(a). That is, increases quickly and then slowly as increases. On the other hand, when the voice traffic is small, the bursty data effect occurs when is large. Thus, in Fig. 6(a), curves are concave (i.e., increases slowly and then quickly as increases).
5) Effects of Voice User Mobility: In Fig. 6(d), the GSM voice user mobility is ten times of that in Fig. 6(a). With a higher mobility, handoffs are more likely to occur in a voice call. How-ever, Fig. 6(a) and (d) indicates that the mobility of voice users does not affect the GPRS data transmission. When the voice user mobility rate increases, the voice users are more likely to move to another cell during the conversation, and two effects are observed.
Effect 1) The channel occupancy times for voice calls be-come shorter.
Effect 2) The voice call handoff arrival rate at a cell be-comes higher.
Effect 1) allows GPRS packets to have a better chance to be served. Effect 2) results in more voice calls to compete radio channels with packets. These two conflicting effects balance against each other. Thus, we observe that voice user mobility has no apparent effect on .
6) Performance of Voice Call Completion: Fig. 7 plots as a function of and , where . Like Fig. 6, Fig. 7 shows the effects of various packet sizes, voice call arrival rates, and GSM voice user mobility rates. A general phenomenon in Fig. 7 is that increases as increases. This result also reflects the bursty data effect as observed in Fig. 6.
7) The Base Case: Consider Fig. 7(a), where the packet size is small ( ) and the voice traffic is low ( ). This figure indicates that increases as increases for . In this case, since voice traffic is low, it is less likely that multiple voice calls will arrive and be processed at the same time. That is, the voice calls do not compete among themselves. Instead, they compete with packet requests. For a larger , the packet traffic becomes more bursty. Therefore, it is more diffi-cult for voice requests to be accepted. When , a packet
(a) (b)
(c) (d)
Fig. 7. Impact of voice call completion for FRA (C = 7). (a)
= 100 ; = ; = 0:2 . (b) = 10 ; = ; = 0:2 . (c) = 100 ; = 5 ; = 0:2 . (d) = 100 ; = ; = 2 .
arrival is dropped if any radio channel is occupied by a voice request or another packet. Thus voice requests have a better chance to be served, and the packets are likely to be blocked as increases from six to seven. Consequently, decreases as increases from six to seven.
8) Effects of Packet Size: In Fig. 7(b), the average packet size is ten times of that in Fig. 7(a). In this case, the offered load of GPRS packets becomes larger, and voice requests are likely to compete with more than one packet request at the same time. The figure indicates that the decrease of is very significant in two cases: when increases from three to four and from six to seven.
1) Since increases significantly as increases from three to four [Fig. 6(b)], the voice requests have a better chance to be served. Thus decreases significantly. This effect is pronounced when is large.
2) We observe local minimum in the curves of Fig. 7(b). The phenomenon is explained as follows. For , when , the system can at most accommodate one packet transmission at a time. In this case, at most three chan-nels are available for voice call requests. Similarly, for , 7 channels can be used for voice calls when a packet is in transmission. Compared with the cases where , , or , more channels are available to serve voice call requests for the case when . For the case where , more than one packet can be processed at a time, and fewer channels are likely to be available for the voice
(a) (b)
(c) (d)
Fig. 8. ComparingP for the resource allocation algorithms ( = 5 ;
C = 7; Q = 7). (a) = 100 ; = ; = 0:2 . (b) = 10 ; = ; = 0:2 . (c) = 100 ; = 5 ; = 0:2 .
(d) = 100 ; = ; = 2 .
call requests as compared with the case where . Thus a local minimum can be observed at for every curve in Fig. 7(b). This phenomenon is ob-served when packet size is large (i.e., ). 3) Following the same reasoning in Fig. 7(a), decreases
as increases from six to seven.
9) Effects of Voice Call Arrival Rate: In Fig. 7(c), the voice traffic is five times of that in Fig. 7(a). In this case, the voice traffic is large and the arrival packets become less competitive compared with the voice requests. Thus packet requests have less chance to be served as increases, and decreases as
increases.
10) Effects of Voice User Mobility: In Fig. 7(d), the GSM voice user mobility is ten times that in Fig. 7(a). With a higher mobility, handoffs are more likely to occur in a voice call. Thus for high mobility [Fig. 7(d)] is larger than that for low mobility [Fig. 7(a)].
It is interesting to note a general trend that both and increase as increases. Thus the operators should think care-fully if they would provide quick GPRS transmission service at the cost of increasing packet and voice call blocking/dropping rates.
B. Comparison for the FRA and DRA Algorithms
This section compares the performance for FRA algorithms (i.e., FRA, FRAQ_N, FRAQ_H, and FRAQ_NH) and DRA
al-(a) (b)
(c) (d)
Fig. 9. ComparingP for the resource allocation algorithms ( = 5 ;
C = 7; Q = 7). (a) = 100 ; = ; = 0:2 . (b) = 10 ; = ; = 0:2 . (c) = 100 ; = 5 ; = 0:2 .
(d) = 100 ; = ; = 2 .
gorithms (i.e., DRA, DRAQ_N, DRAQ_H, and DRAQ_NH). In our study, the buffer size of the waiting queue is .
1) Effects of Dynamic and Fixed Allocations: Figs. 8 and 9 plot and as functions of . The parameter setups in these two figures are the same as in Fig. 6. Fig. 8 indicates that in terms of the performance, DRA algorithms (with or without queuing) always outperform FRA algorithms (with or without queuing). This result is explained as follows. By partially al-locating resources to packet transmissions, dynamic allocation can accommodate more packet requests than fixed allocation does. Fig. 9 indicates that in terms of , the results are oppo-site to that in Fig. 8. It is interesting to note that FRAQ_NH and DRAQ_NH have similar performance that is much better than other algorithms. Since both new calls and handoff calls can be buffered and have better opportunity to survive, small
for both FRAQ_NH and DRAQ_NH are expected. 2) Effects of the Queuing Mechanisms: Fig. 9 indicates that queuing mechanisms may significantly affect the perfor-mance. When voice user mobility is low [i.e., in Fig. 9(a)–(c)], the performance for fixed allocation from the best to the worst are FRAQ_NH, FRAQ_N, FRAQ_H, and FRA. When the voice user mobility is high (i.e., in Fig. 9(d)), the performance from the best to the worst are FRAQ_NH, FRAQ_H, FRAQ_N, and FRA. With small , it is more effective to buffer new calls, and FRAQ_N outperforms FRAQ_H. On the other hand, when is large, FRAQ_H
out-performs FRAQ_N. Same results are observed for dynamic al-location algorithms. Fig. 8(a), (b), and (d) indicate that when the voice call arrival rate is small (i.e., ), is not affected by the queuing mechanisms. When the voice call arrival rate is large [ in Fig. 8(c)], the performance from the best to the worst are FRA (DRA), FRAQ_H (DRAQ_H), FRAQ_N (DRAQ_N), and FRAQ_NH (DRAQ_NH). This order is oppo-site to the results observed in Fig. 9(c).
Figs. 8 and 9 indicate that DRAQ_NH outperforms other al-gorithms in terms of and performance.
C. Effects of the Variations of the Distributions for Input Parameters
This section studies the effects of the variances of the distri-butions for packet transmission times, packet interarrival times and cell residence times for GSM voice users. We consider DRAQ_NH in this section. Results for other algorithms are similar and are omitted. We assume that packet transmission times, packet interval times, and cell residence times for GSM voice users have Gamma distributions with means , ,
and and variances , , and
, respectively, where , , and are the shape parameters. Gamma distributions are considered be-cause they can be used to approximate many other distributions as well as measured data from GSM field trials. Fig. 10 plots
and as functions of , where , ,
, , , and . To investigate
the variance of the distribution for one input parameter, the distributions for the other two parameters are set to exponential (i.e., the shape parameters are set to one). For example, in Fig. 10(a), the distribution for the packet transmission times is Gamma, and the distributions for the packet interarrival times and voice user cell residence times are exponential. We note that the data packet transmission times are often modeled by Pareto distributions. In terms of variance impact, both Pareto and Gamma show the same trend. To be consistent, we use Gamma distributions for the three input parameters.
1) Variance of Packet Transmission Times: In Fig. 10(a) and (b), packet transmission times have Gamma distributions
with variances , , and , respectively.
The two figures indicate that and are insensitive to the variance of packet transmission times. As proven by the Zachary–Kelly model [15], [10], for FRA, when the voice calls and packet arrivals are Poisson streams, the packet dropping probability and the voice blocking probability are not affected by the distributions of the packet sizes and call holding times and are only affected by the means of the packet sizes and call holding times. Our simulation experiments indicated that DRAQ_NH and other algorithms also preserve this property.
2) Variance of Packet Interarrival Times: In Fig. 10(c) and (d), the packet interarrival times are Gamma distributed with
variances , , and ,
re-spectively. Fig. 10(d) indicates that is not affected by . In Fig. 10(c), we observe the following.
1) increases as increases.
2) When , increases as increases.
(a) (b)
(c) (d)
(e) (f)
Fig. 10. Effects of the variances of packet transmission times, packet interarrival times, and GSM voice user cell residence times (DRAQ_NH;
= 5 ; = 5 ; = 100 ; = 0:2 ; C = 7; Q = 7).
(a) Gamma distributed packet transmission times. (b) Gamma distributed packet transmission times. (c) Gamma distributed packet interarrival times. (d) Gamma distributed packet interarrival times. (e) Gamma distributed GSM voice-user cell residence times. (f) Gamma distributed GSM voice-user cell residence times.
Phenomenon 1) indicates that with a larger variance , more small packet interarrival times are observed. Thus more packets arrive in a short period, and the packet traffic becomes more bursty. Phenomenon 2) states that the bursty effect due to the increase of becomes insignificant when the variance is small.
3) Variance of Cell Residence Times for GSM Voice Users: In Fig. 10(e) and (f), GSM voice user cell residence times are Gamma distributed with variances , , and , respectively. These figures indicate that:
1) decreases as increases; 2) increases as increases.
The above results indicate that with a larger , more short cell residence times for GSM voice users are observed. Thus voice calls are more likely to hand off to another cell, and voice handoff traffic becomes more bursty. Consequently, voice calls become less likely to be completed. On the other hand, packet data requests have better chance to be accepted in this case.
(a) (b)
(c) (d)
Fig. 11. The average number of channels for a served packet in DRAQ_NH (C = 7; Q = 7). (a) = 100 ; = ; = 0:2 . (b) =
10 ; = ; = 0:2 . (c) = 100 ; = 5 ; = 0:2 .
(d) = 100 ; = ; = 2 .
D. The Average Number of Channels Assigned to Packet Transmission
By allocating partial resources to packet transmissions, dy-namic allocation accommodates more packet requests. How-ever, the number of channels allocated to a packet data request may be smaller than . Consequently, a packet data is trans-mitted at a slower rate than that in fixed allocation. In this sec-tion, we evaluate the average number of channels for a served packet in DRAQ_NH. Fig. 11 plots as a function of with the same input parameter setups of the experiments in Fig. 8. We observe the following.
1) In Fig. 11(a), (b), and (d), the voice call arrival rate ( ) is small and decreases as increases. With a small call arrival rate, when increases, it is more likely that the BS processes multiple packets at the same time, and thus the channels of the BS are shared by multiple packets. This phenomenon is pronounced when the packet transmission times become large, as shown in Fig. 11(b).
2) In Fig. 11(c), the voice call arrival rate ( ) is large. In this case, is not significantly affected by an in-creasing . This phenomenon indicates that when voice call arrival rate is large, the voice call requests are more likely to be buffered before being served, and thus the voice traffic becomes more bursty. In this case, packets
Fig. 12. The average waiting time for the accepted voice call requests in DRAQ_NH ( = 100 ; = ; = 0:2 ; C = 7; Q = 7).
compete with a large number of voice calls, and poor performance is observed for .
E. The Average Waiting Time for the Accepted Voice Call Requests
The buffering mechanism for voice calls can effectively re-duce . In this section, we evaluate the average waiting time for the accepted voice call requests in DRAQ_NH. Fig. 12 plots as a function of with the same input parameter values for the experiments in Fig. 8. We observe the following. 1) For most cases in Fig. 12, the values are below 10 , which implies that the accepted voice calls are served with short waiting times. Thus, the buffering mechanism effectively improves the voice system per-formance by slightly increasing the waiting time. 2) When is small (i.e., and in Fig. 12),
the packet data traffic is low and the effect of (i.e., burstness of traffic) is not significant. In this case, is only slightly affected by the change of .
3) When becomes large (i.e., and
), increases as increases. That is, when packet data traffic becomes high, the effect of bursty data traffic becomes significant, and is an increasing function of .
V. CONCLUSION
This paper studied the impact of GPRS service on the GSM network. Specifically, we proposed analytic and simulation models to investigate the performance for GPRS and GSM networks. We considered fixed and dynamic GPRS resource allocation algorithms as specified in the GPRS standard. We also proposed to include a waiting queue that buffers the voice requests when no radio channel is available. Our study indicated that dynamic allocation effectively increases the GPRS packet acceptance rate, and the queuing mechanism significantly reduces the voice call incompletion probability. By integrating both mechanisms, the best packet/voice call acceptance is expected. Our study also indicated that if too many channels are allocated to a packet transmission, both packet and voice call droppings will increase. Thus the operator should think
carefully if he would provide quick GPRS transmission service at the cost of decreasing packet/voice call acceptance rates.
In terms of GPRS data performance, this paper studied the packet dropping effect, that is, performance of radio resource allocation at GPRS MAC layer. Our study can be extended to in-vestigate the management of GPRS session at higher layer pro-tocols (i.e., session management layer and TCP), where certain average bandwidth may be guaranteed for GPRS data transmis-sion.
ACKNOWLEDGMENT
The authors would like to thank the three anonymous reviewers who provided valuable comments to improve the quality of this paper.
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Phone Lin received his B.S.C.S.I.E. degree from
National Chiao Tung University, Taiwan, R.O.C., in 1996, where he is currently pursuing the Ph.D. degree in the Department of Computer Science and Information Engineering.
His current research interests include personal communications services, mobile computing, and performance modeling.
Yi-Bing Lin (SM’98) received the B.S.E.E. degree
from National Cheng Kung University, Taiwan, R.O.C., in 1983 and the Ph.D. degree in computer science from the University of Washington, Seattle, in 1990.
From 1990 to 1995, he was with the Applied Research Area at Bell Communications Research (Bellcore), Morristown, NJ. In 1995, he became a Professor in the Department of Computer Science and Information Engineering (CSIE), National Chiao Tung University (NCTU). In 1996, he became Deputy Director of the Microelectronics and Information Systems Research Center, NCTU. During 1997–1999, he became Chairman of CSIE, NCTU. He is an editor of Computer Networks, an area editor of ACM Mobile Computing
and Communication Review, a columnist of ACM Simulation Digest, an
editor of International Journal of Communications Systems, an editor of
ACM/Baltzer Wireless Networks, an editor of Computer Simulation Modeling and Analysis, an editor of Journal of Information Science and Engineering.
He was Guest Editor for the ACM/Baltzer MONET Special Issue on Personal
Communications. He is the coauthor of the book Wireless and Mobile Network Architecture (New York: Wiley). His current research interests include design
and analysis of personal communications services network, mobile computing, distributed simulation, and performance modeling.
Dr. Lin is an Associate Editor of IEEE Network, an editor of IEEE JOURNAL OFSELECTEDAREAS OFCOMMUNICATION: Wireless Series, and an editor of
IEEE Personal Communications Magazine. He was a Guest Editor for IEEE
TRANSACTIONS ON COMPUTERSSpecial Issue on Mobile Computing, and a
Guest Editor for IEEE Communications Magazine Special Issue on Active,
Programmable, and Mobile Code Networking. He was Program Chair for the 8th Workshop on Distributed and Parallel Simulation, General Chair for the 9th Workshop on Distributed and Parallel Simulation, and Program Chair for
the 2nd International Mobile Computing Conference. He received 1998 and 2000 Outstanding Research Awards from National Science Council, R.O.C. and 1998 Outstanding Youth Electrical Engineer Award from CIEE, R.O.C. He is an Adjunct Research Fellow of Academia Sinica.
