Delay Tolerant Voice Calls in a GSMGPRS Cell

1
University of Glamorgan Mobile Computing and
Networking Research Centre
Performance Modelling with MOSEL-2

• Delay Tolerant Voice Calls in a GSM/GPRS Cell

Patrick Wuechner 1,2, Khalid Al-Begain 1, Joerg
Barner 2, Gunter Bolch 2 1 University of
Glamorgan, Wales, UK 2 University of
Erlangen, Germany
2
Outline

• Introduction
• Performance Modelling with MOSEL-2
• A single GSM/GPRS Cell with Delay Tolerant Voice
  Calls (DeTVoC)
• Recent Improvements of MOSEL-2

3
Introduction

• MOSEL (Modelling, Specification, and Evaluation
  Language) is a textual high-level modelling
  language.
• Developed in Erlangen.
• Suitable for describing system model based on
  queuing networks, Petri Nets, and many else.
• MOSEL Package contains Language Interpreter,
  Numerical/simulation solvers, and graphical tool
  for result presentation.

4
Introduction

• History of MOSEL
• MOSLANG (predecessor of MOSEL)
• MOSEL (H. Herold, G. Bolch, K.Al-Begain)
• Markov solution only
• C based syntax and support
• Support for SPNP and MOSES tools
• MOSEL-2 (B. Beutel, J. Barner, G.Bolch)
• Markov and DSPN based solution (immediate,
  exponential and deterministic transitions)
• Simulation
• Moved away from C
• Support for SPNP and MOSES tools
• Next MOSEL (P. Wuechner, K.Al-Begain)
• Empirical and General distributions
• ???

5
MOSEL-2 A Basic Example

• Closed Tandem Network
• Petri Net model description

Exp
Det
p2
p1
N3
6
MOSEL-2 A Basic Example

• Closed Tandem Network
• MOSEL model description

Exp
Det
p2
p1
N3
1 PARAMETER rate_t1 2 .. 8 STEP 2 2 CONST
mean_t2 1/5 3 NODE p13 2 4 NODE
p23 1 5 FROM p1 TO p2 RATE rate_t1 6
FROM p2 TO p1 AFTER mean_t2 7 PRINT avg_in_p1
MEAN(p1)
7
MOSEL-2 A Basic Example

• Closed Tandem Network
• MOSEL model description

Exp
Det
p2
p1
N3
1 PARAMETER rate_t1 2 .. 8 STEP 2 2 CONST
mean_t2 1/5 3 NODE p13 2 4 NODE
p23 1 5 FROM p1 TO p2 RATE rate_t1 6
FROM p2 TO p1 AFTER mean_t2 7 PRINT avg_in_p1
MEAN(p1)
Parameter Part
8
MOSEL-2 A Basic Example

• Closed Tandem Network
• MOSEL model description

Exp
Det
p2
p1
N3
1 PARAMETER rate_t1 2 .. 8 STEP 2 2 CONST
mean_t2 1/5 3 NODE p13 2 4 NODE
p23 1 5 FROM p1 TO p2 RATE rate_t1 6
FROM p2 TO p1 AFTER mean_t2 7 PRINT avg_in_p1
MEAN(p1)
System State Definition Part
9
MOSEL-2 A Basic Example

• Closed Tandem Network
• MOSEL model description

Exp
Det
p2
p1
N3
1 PARAMETER rate_t1 2 .. 8 STEP 2 2 CONST
mean_t2 1/5 3 NODE p13 2 4 NODE
p23 1 5 FROM p1 TO p2 RATE rate_t1 6
FROM p2 TO p1 AFTER mean_t2 7 PRINT avg_in_p1
MEAN(p1)
Transition Rules Part
10
MOSEL-2 A Basic Example

• Closed Tandem Network
• MOSEL model description

Exp
Det
p2
p1
N3
1 PARAMETER rate_t1 2 .. 8 STEP 2 2 CONST
mean_t2 1/5 3 NODE p13 2 4 NODE
p23 1 5 FROM p1 TO p2 RATE rate_t1 6
FROM p2 TO p1 AFTER mean_t2 7 PRINT avg_in_p1
MEAN(p1)
Result definition part
11
MOSEL-2 Invoking the Environment

• Command line
• Options
• -T Translate MOSEL model to TimeNET model.
• (can be c for SPNP or m for Moses)
• -s Start appropriate tool (TimeNET)
  automatically.

mosel2 Ts tandem.mos
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MOSEL-2 Workflow
real system

• building MOSEL-2 system description and starting
  the environment
• MOSEL-2 translates the given model to the input
  file format of an evaluation tool
• the appropriate tool is called by MOSEL-2
• the tool evaluates the model either using
  numerical analysis methods or discrete event
  simulation
• tool writes it output to tool specific output
  files
• MOSEL-2 collects and parses all output files to
  uniform result files

user
1
1
sys.mos
2
2
sys.m
sys.c
sys.tn
sys.?

3
3
MOSES
SPNP
TimeNET
other

4
4
discrete event simulation
numerical analysis
5
5
tool
specific
result
files

6
6
sys.res, igl
13
MOSEL-2 Result Presentation

• textual

• graphical(if specified)

Stationary analysis of "tandem.mos" by
TimeNET Parameters rate_t1 2 Results
avg_in_p1 2.49505
Parameters rate_t1
4 Results avg_in_p1 1.80837
Parameters
rate_t1 6 Results avg_in_p1
1.20243
Parameters rate_t1 8 Results
avg_in_p1 0.818239
14
GSM/GPRS Cell with Delay Tolerant Voice Calls

• Assumptions
• N GSM channels shared between Voice and data
  traffic.
• Voice is circuit-switched.
• Data is packet switched (can be buffered).
• Data traffic utilises all channels not used by
  Voice.
• When all channels are busy Voice calls are
  blocked but NOT lost immediately.
• Blocked voice calls are delayed for a certain
  (fixed) amount of time before being rejected.

15
DSPN model of GSM/GPRS air interface
t1 Poisson voice arrival processt2 Poisson
data arrival processt3 data losst4 data
admissiont5 call admissiont6 DeTVoC
(deterministic, IS)t7 data service
(exponential, IS)t8 voice service (exponential)
D
V

t1
t2
t3
p1
p2
TDMA
t7
t4
p3
t5
t8
p4
t6

D
V
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MOSEL-2 Model
01 / PARAMETER AND CONSTANTS
/ 02 PARAMETER lambda_d 0.1, 0.5 .. 2.5
STEP 0.25 03 CONST lambda_v 1/100 04
CONST mue_single_v 1/80 05 CONST
max_users_v 100 06 CONST chan_res_d
1 07 CONST waiting_time 10 08 CONST
mue_single_d (21.4/8) / 10 09 10 / NODES
/ 11 NODE
p1max_users_v 0 12 NODE p21
0 13 NODE p332 0 14
NODE p4chans-chan_res_d 0 15 16 /
TRANSITIONS / 17
FROM EXTERN TO p1 RATE lambda_v
//t1 18 FROM EXTERN TO p2 RATE lambda_d
//t2 19 FROM p2 TO EXTERN PRIO 1
//t3 20 FROM p2 TO p3 PRIO 2
//t4 21 FROM p1 TO p4 PRIO 2
//t5 22 _at_lt1..max_users_vgt
//t6 23 IF p1 gt FROM p1
24 TO EXTERN 25 AFTER
waiting_time 26 PRIO 1 27
28 FROM p3 TO EXTERN RATE mue_single_d (8-p4)
//t7 29 FROM p4 TO EXTERN RATE mue_single_v p4
//t8 30 31 / RESULTS
/ 32 // TEXTUAL (.res) 33 PRINT
d_loss PROB (p332) 34 PRINT v_block
UTIL (p1) 35 36 // GRAPHICAL (.igl) 37
PICTURE prob. of data loss and voice
blocking" 38 PARAMETER lambda_d 39 XLABEL
"incoming burst rate" 40 YLABEL "PROB" 41 CURVE
d_loss 42 CURVE v_block
17
MOSEL-2 Results
18
MOSEL-2 Results
19
MOSEL-2 Recent Improvements

• Introducing automatic approximation of
  empirical distributions
• MOSEL
• Petri Net
• 3 different approximations depending on Squared
  Coefficient of Variation

20
MOSEL-2 Recent Improvements

• c2 1Empirical distribution gets substituted by
  Exponential distribution with service rate

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MOSEL-2 Recent Improvements

• c2 gt 1Empirical distribution gets substituted by
  Generalized Exponential (GE) construct

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MOSEL-2 Recent Improvements

• c2 lt 1Empirical distribution gets substituted by
  Hypoexponential Phase-Type (PH) construct

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MOSEL-2 Application revisited

• ESPN model of GSM/GPRS air interface

t1 Poisson voice arrival processt2 Poisson
data arrival processt3 data losst4 data
admissiont5 call admissiont6 DeTVoC (exp
delay)t7 data service (empirical, IS)t8 voice
service (exponential)
t3
D
V

t7
t1
t2
p1
p2
TDMA
t4
p3
t5
t8
p4
t6

D
V
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MOSEL-2 Model
1 / PARAMETER AND CONSTANTS
/ 2 CONST lambda_d 1.5 3 PARAMETER
lambda_v 0.02 .. 0.06 STEP 0.01 4 CONST
mue_single_v 1/80 5 CONST max_users_v
50 6 CONST chans 8 7 CONST
chan_res_d 1 8 CONST chan_max_d
chans - 2 9 CONST waiting_time 10 10
CONST mean_single_d 10 / (21.4/8) 11
PARAMETER scv_d 0.5, 1, 2 12 CONST var_d
scv_d mean_single_d 13
mean_single_d 14 15 / NODES
/ 16 NODE
p1max_users_v 0 17 NODE p21
0 18 NODE p332 0 19
NODE p4chans-chan_res_d 0 20 21 /
TRANSITIONS / 22
FROM EXTERN TO p1 RATE lambda_v
//t1 23 FROM EXTERN TO p2 RATE lambda_d
//t2 24 FROM p2 TO EXTERN PRIO 1
//t3 25 FROM p2 TO p3 PRIO 2
//t4 26 FROM p1 TO p4 PRIO 2
//t5 27 FROM p1 TO EXTERN RATE
//t6 28 p1(1/WAITING_TIME) PRIO
1 29 30
31 _at_lt1..chan_max_dgt
//t7 32 IF (chans-p4) gt 33 FROM p3 TO
EXTERN EMP (mean_single_d, var_d) 34 35 FROM
p4 TO EXTERN RATE mue_single_v p4
//t8 36 37 / RESULTS
/ 38 // TEXTUAL (.res) 39 PRINT d_loss
PROB (p332) 40 PRINT v_block
UTIL (p1) 41 42 PRINT data_mean
MEAN (p3) 43 PRINT voice_mean MEAN
(p4) 44 PRINT voice_mean_w MEAN
(p1) 45 46 // GRAPHICAL (.igl) 47 48 PICTURE
"data burst loss and voice blocking" 49
PARAMETER lambda_V 50 XLABEL "incoming burst
rate" 51 YLABEL "PROB" 52 CURVE d_loss 53
54 55 PICTURE Voice Blocking Probability" 56
PARAMETER lambda_v 57 XLABEL "incoming burst
rate" 58 YLABEL PROB" 59 CURVE d_loss 60 61
25
MOSEL-2 Results 1
26
MOSEL-2 Results 2
27
Conclusion

• MOSEL is growing and getting more and more
  interesting features
• Increased modelling power
• Unfortunately, the new features limit the size of
  the model because of new nodes added.
• We hope to start a new project on a new version
  of MOSEL that will be very powerful tool with
  many new features.