Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
"""
Comparison utilities for analytical vs simulation results.
"""
from typing import Dict, Tuple
from dataclasses import dataclass
from .jackson import JacksonAnalyzer, NetworkAnalytics
from ..core.simulation import SimulationResults
@dataclass
class QueueComparison:
"""Comparison of analytical vs simulation for a single queue."""
queue_id: str
# Analytical
analytical_utilization: float
analytical_avg_customers: float
analytical_avg_time: float
analytical_avg_wait: float
# Simulation
simulation_utilization: float
simulation_avg_customers: float
simulation_avg_time: float
simulation_avg_wait: float
# Differences (%)
utilization_diff_percent: float
avg_customers_diff_percent: float
avg_time_diff_percent: float
avg_wait_diff_percent: float
@dataclass
class NetworkComparison:
"""Complete comparison of analytical vs simulation results."""
is_stable: bool
coordinator: QueueComparison
servers: Dict[str, QueueComparison]
# System-wide
analytical_total_L: float
analytical_total_W: float
simulation_total_L: float
simulation_total_W: float
total_L_diff_percent: float
total_W_diff_percent: float
def calculate_percentage_difference(analytical: float, simulation: float) -> float:
"""
Calculate percentage difference: ((simulation - analytical) / analytical) * 100
Args:
analytical: Analytical value
simulation: Simulation value
Returns:
Percentage difference
"""
if analytical == 0:
return 0.0 if simulation == 0 else 100.0
return ((simulation - analytical) / analytical) * 100.0
def compare_queue(
queue_id: str,
analytical: 'QueueAnalytics',
simulation: Dict
) -> QueueComparison:
"""
Compare analytical vs simulation results for a single queue.
Args:
queue_id: Queue identifier
analytical: QueueAnalytics from Jackson's theorem
simulation: Simulation statistics dict
Returns:
QueueComparison with all metrics
"""
# Handle unstable queues
if not analytical.is_stable:
analytical_L = float('inf')
analytical_W = float('inf')
analytical_Wq = float('inf')
else:
analytical_L = analytical.average_customers
analytical_W = analytical.average_time
analytical_Wq = analytical.average_wait_time
simulation_rho = simulation['utilization']
simulation_W = simulation['average_system_time']
simulation_Wq = simulation['average_wait_time']
# Estimate L from simulation using Little's Law: L = λ * W
simulation_L = analytical.arrival_rate * simulation_W if analytical.arrival_rate > 0 else 0
return QueueComparison(
queue_id=queue_id,
analytical_utilization=analytical.utilization,
analytical_avg_customers=analytical_L,
analytical_avg_time=analytical_W,
analytical_avg_wait=analytical_Wq,
simulation_utilization=simulation_rho,
simulation_avg_customers=simulation_L,
simulation_avg_time=simulation_W,
simulation_avg_wait=simulation_Wq,
utilization_diff_percent=calculate_percentage_difference(
analytical.utilization, simulation_rho
),
avg_customers_diff_percent=calculate_percentage_difference(
analytical_L, simulation_L
),
avg_time_diff_percent=calculate_percentage_difference(
analytical_W, simulation_W
),
avg_wait_diff_percent=calculate_percentage_difference(
analytical_Wq, simulation_Wq
)
)
def compare_results(
analytical: NetworkAnalytics,
simulation: SimulationResults
) -> NetworkComparison:
"""
Compare complete analytical vs simulation results.
Args:
analytical: NetworkAnalytics from Jackson's theorem
simulation: SimulationResults from simulation
Returns:
NetworkComparison with all metrics
"""
# Compare coordinator
coordinator_comp = compare_queue(
"coordinator",
analytical.coordinator,
simulation.coordinator_stats
)
# Compare servers
server_comps = {}
for server_id, server_analytical in analytical.servers.items():
server_simulation = simulation.server_stats[server_id]
server_comps[server_id] = compare_queue(
server_id,
server_analytical,
server_simulation
)
# System-wide comparison
simulation_total_W = simulation.average_system_time
# Estimate total L using Little's Law: L = λ₀ × W
# IMPORTANT: Use external arrival rate λ₀, NOT coordinator effective rate γ₀
external_lambda = analytical.external_arrival_rate
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
simulation_total_L = external_lambda * simulation_total_W if external_lambda > 0 else 0
return NetworkComparison(
is_stable=analytical.is_stable,
coordinator=coordinator_comp,
servers=server_comps,
analytical_total_L=analytical.total_average_customers,
analytical_total_W=analytical.total_average_time,
simulation_total_L=simulation_total_L,
simulation_total_W=simulation_total_W,
total_L_diff_percent=calculate_percentage_difference(
analytical.total_average_customers,
simulation_total_L
),
total_W_diff_percent=calculate_percentage_difference(
analytical.total_average_time,
simulation_total_W
)
)
def print_comparison(comparison: NetworkComparison) -> None:
"""Print a formatted comparison report."""
print("=" * 80)
print("ANALYTICAL VS SIMULATION COMPARISON")
print("=" * 80)
print(f"\n🌐 System-Wide Metrics:")
print(f" {'Metric':<20} {'Analytical':<15} {'Simulation':<15} {'Diff %':<10}")
print(" " + "-" * 60)
print(f" {'Total L (customers)':<20} {comparison.analytical_total_L:<15.4f} "
f"{comparison.simulation_total_L:<15.4f} {comparison.total_L_diff_percent:>9.2f}%")
print(f" {'Total W (time)':<20} {comparison.analytical_total_W:<15.4f} "
f"{comparison.simulation_total_W:<15.4f} {comparison.total_W_diff_percent:>9.2f}%")
print(f"\n📊 Coordinator Queue:")
coord = comparison.coordinator
print(f" {'Metric':<20} {'Analytical':<15} {'Simulation':<15} {'Diff %':<10}")
print(" " + "-" * 60)
print(f" {'Utilization (ρ)':<20} {coord.analytical_utilization:<15.4f} "
f"{coord.simulation_utilization:<15.4f} {coord.utilization_diff_percent:>9.2f}%")
print(f" {'Avg customers (L)':<20} {coord.analytical_avg_customers:<15.4f} "
f"{coord.simulation_avg_customers:<15.4f} {coord.avg_customers_diff_percent:>9.2f}%")
print(f" {'Avg time (W)':<20} {coord.analytical_avg_time:<15.4f} "
f"{coord.simulation_avg_time:<15.4f} {coord.avg_time_diff_percent:>9.2f}%")
print(f" {'Avg wait (Wq)':<20} {coord.analytical_avg_wait:<15.4f} "
f"{coord.simulation_avg_wait:<15.4f} {coord.avg_wait_diff_percent:>9.2f}%")
for server_id, server_comp in comparison.servers.items():
print(f"\n📊 {server_id}:")
print(f" {'Metric':<20} {'Analytical':<15} {'Simulation':<15} {'Diff %':<10}")
print(" " + "-" * 60)
print(f" {'Utilization (ρ)':<20} {server_comp.analytical_utilization:<15.4f} "
f"{server_comp.simulation_utilization:<15.4f} {server_comp.utilization_diff_percent:>9.2f}%")
print(f" {'Avg customers (L)':<20} {server_comp.analytical_avg_customers:<15.4f} "
f"{server_comp.simulation_avg_customers:<15.4f} {server_comp.avg_customers_diff_percent:>9.2f}%")
print(f" {'Avg time (W)':<20} {server_comp.analytical_avg_time:<15.4f} "
f"{server_comp.simulation_avg_time:<15.4f} {server_comp.avg_time_diff_percent:>9.2f}%")
print(f" {'Avg wait (Wq)':<20} {server_comp.analytical_avg_wait:<15.4f} "
f"{server_comp.simulation_avg_wait:<15.4f} {server_comp.avg_wait_diff_percent:>9.2f}%")
print("\n" + "=" * 80)
print("✅ Comparison complete")
print("=" * 80)