4.2 Results
5.1.5 Finite-size effects
The input data in Tables 14 and 16 to 19 enable derivation of more information (responses from the input variables) for evaluating the performance of the waste management system. The three dumpsites were juxtaposed in columns set as shown in Table 4 but have been presented here in separate tables for want of space.
As can be seen from Table 14, even though the overall waste evacuation efficiency (88.8%) at Ogbalingba dumpsite is commendable, the system still showed not to be stable as λ > μ.
Table 14: Data collected on solid waste generation and evacuation processes in Ogbalingba ' dumpsite of Awka city, Anambra State
Time Ogbalingba Dumpsite (No. Of Chain-up Bins = 3)
Days
Lq qd
(Nq=0)d
qN
(cb) (Nq=0)N
q NtGL
λq μq
Nμ=0
Lw Ls Wa Wq Ws
η (%) P(t)λ
Cum P(t)λ (d+N)
(cb) (cb) (cbpd) (cb) (hrs)
1 2.0 0.2 0 0.3 0 0.5 0 2.2 0 1 2.2 2.5 24 21.8 27.3 0.0 0.008 0.008
2 2.5 0.2 0 0.5 0 0.7 0 2.7 0 1 2.7 3.2 48 22.2 28.4 0.0 0.010 0.018
3 3.2 0.5 0 0.0 1 0.5 0 3.7 0 1 3.7 3.7 72 20.8 24.0 0.0 0.014 0.032
4 3.7 0.2 0 0.4 0 0.6 0 3.9 3 0 0.9 4.3 24 22.8 26.5 76.9 0.015 0.047
5 1.3 0.4 0 0.5 0 0.9 1 1.7 0 1 1.7 2.2 24 18.4 31.1 0.0 0.006 0.054
6 2.2 0.0 1 0.8 0 0.8 0 2.2 0 1 2.2 3.0 48 24.0 32.7 0.0 0.008 0.062
7 3.0 0.2 0 0.0 1 0.2 0 3.2 0 1 3.2 3.2 72 22.5 24.0 0.0 0.012 0.074
8 3.2 0.9 0 0.8 0 1.7 0 4.1 2 0 2.1 4.9 24 18.7 28.7 48.8 0.015 0.089
9 2.9 0.4 0 0.0 1 0.4 1 3.3 0 1 3.3 3.3 24 21.1 24.0 0.0 0.012 0.102
10 3.3 0.2 0 0.6 0 0.8 0 3.5 0 1 3.5 4.1 48 22.6 28.1 0.0 0.013 0.115
11 4.1 0.2 0 0.5 0 0.7 0 4.3 2 0 2.3 4.8 24 22.9 26.8 46.5 0.016 0.131
12 2.8 0.0 1 0.5 0 0.5 0 2.8 0 1 2.8 3.3 24 24.0 28.3 0.0 0.011 0.142
13 3.3 0.2 0 0.6 0 0.8 1 3.5 0 1 3.5 4.1 48 22.6 28.1 0.0 0.013 0.155
14 4.1 0.4 0 0.4 0 0.8 0 4.5 0 1 4.5 4.9 72 21.9 26.1 0.0 0.017 0.172
15 4.9 0.2 0 0.5 0 0.7 0 5.1 0 1 5.1 5.6 96 23.1 26.4 0.0 0.019 0.191
16 5.6 0.2 0 0.8 0 1.0 0 5.8 3 0 2.8 6.6 24 23.2 27.3 51.7 0.022 0.213
147
17 3.6 0.4 0 0.2 0 0.6 1 4.0 0 1 4.0 4.2 24 21.6 25.2 0.0 0.015 0.228
18 4.2 0.0 1 0.7 0 0.7 0 4.2 0 1 4.2 4.9 48 24.0 28.0 0.0 0.016 0.244
19 4.9 0.4 0 0.0 1 0.4 0 5.3 0 1 5.3 5.3 72 22.2 24.0 0.0 0.020 0.264
20 5.3 0.2 0 0.5 0 0.7 0 5.5 3 0 2.5 6.0 24 23.1 26.2 54.5 0.021 0.284
21 3.0 0.3 0 0.3 0 0.6 0 3.3 0 1 3.3 3.6 24 21.8 26.2 0.0 0.012 0.297
22 3.6 0.2 0 0.5 0 0.7 1 3.8 0 1 3.8 4.3 48 22.7 27.2 0.0 0.014 0.311
23 4.3 0.3 0 0.0 1 0.3 0 4.6 1 0 3.6 4.6 24 22.4 24.0 21.7 0.017 0.329
24 3.6 0.1 0 0.8 0 0.9 0 3.7 0 1 3.7 4.5 24 23.4 29.2 0.0 0.014 0.343
25 4.5 0.3 0 0.7 0 1.0 0 4.8 0 1 4.8 5.5 48 22.5 27.5 0.0 0.018 0.361
26 5.5 0.2 0 0.3 0 0.5 0 5.7 1 0 4.7 6.0 24 23.2 25.3 17.5 0.021 0.382
27 5.0 0.1 0 0.0 1 0.1 1 5.1 0 1 5.1 5.1 24 23.5 24.0 0.0 0.019 0.401
28 5.1 0.3 0 0.3 0 0.6 0 5.4 0 1 5.4 5.7 48 22.7 25.3 0.0 0.020 0.422
29 5.7 0.2 0 0.2 0 0.4 0 5.9 3 0 2.9 6.1 24 23.2 24.8 50.8 0.022 0.444
30 3.1 0.2 0 0.4 0 0.6 0 3.3 0 1 3.3 3.7 24 22.5 26.9 0.0 0.012 0.456
31 3.7 0.2 0 0.0 1 0.2 0 3.9 0 1 3.9 3.9 48 22.8 24.0 0.0 0.015 0.471
32 3.9 0.3 0 0.4 0 0.7 0 4.2 3 0 1.2 4.6 24 22.3 26.3 71.4 0.016 0.487
33 1.6 0.2 0 0.0 1 0.2 0 1.8 0 1 1.8 1.8 24 21.3 24.0 0.0 0.007 0.494
34 1.8 0.2 0 0.6 0 0.8 1 2.0 0 1 2.0 2.6 48 21.6 31.2 0.0 0.008 0.501
35 2.6 0.4 0 0.0 1 0.4 0 3.0 0 1 3.0 3.0 72 20.8 24.0 0.0 0.011 0.512
36 3.0 0.7 0 0.8 0 1.5 0 3.7 2 0 1.7 4.5 24 19.5 29.2 54.1 0.014 0.526
37 2.5 0.3 0 0.0 1 0.3 0 2.8 0 1 2.8 2.8 24 21.4 24.0 0.0 0.011 0.537
38 2.8 0.1 0 0.6 0 0.7 1 2.9 0 1 2.9 3.5 48 23.2 29.0 0.0 0.011 0.548
39 3.5 0.3 0 0.5 0 0.8 0 3.8 0 1 3.8 4.3 72 22.1 27.2 0.0 0.014 0.562
40 4.3 0.2 0 0.5 0 0.7 0 4.5 2 0 2.5 5.0 24 22.9 26.7 44.4 0.017 0.579
41 3.0 0.1 0 0.6 0 0.7 0 3.1 0 1 3.1 3.7 24 23.2 28.6 0.0 0.012 0.591
42 3.7 0.3 0 0.4 0 0.7 1 4.0 0 1 4.0 4.4 48 22.2 26.4 0.0 0.015 0.606
43 4.4 0.2 0 0.5 0 0.7 0 4.6 2 0 2.6 5.1 24 23.0 26.6 43.5 0.017 0.623
44 3.1 0.2 0 0.8 0 1.0 0 3.3 0 1 3.3 4.1 24 22.5 29.8 0.0 0.012 0.636
45 4.1 0.4 0 0.2 0 0.6 0 4.5 0 1 4.5 4.7 48 21.9 25.1 0.0 0.017 0.653
46 4.7 0.0 1 0.7 0 0.7 1 4.7 0 1 4.7 5.4 72 24.0 27.6 0.0 0.018 0.670
47 5.4 0.4 0 0.0 1 0.4 0 5.8 0 1 5.8 5.8 96 22.3 24.0 0.0 0.022 0.692
48 5.8 0.2 0 0.5 0 0.7 0 6.0 0 1 6.0 6.5 120 23.2 26.0 0.0 0.023 0.715
49 6.5 0.2 0 0.3 0 0.5 0 6.7 3 0 3.7 7.0 24 23.3 25.1 44.8 0.025 0.740
50 4.0 0.0 1 0.5 0 0.5 0 4.0 0 1 4.0 4.5 24 24.0 27.0 0.0 0.015 0.755
51 4.5 0.2 0 0.0 1 0.2 0 4.7 0 1 4.7 4.7 48 23.0 24.0 0.0 0.018 0.773
52 4.7 0.4 0 0.8 0 1.2 1 5.1 0 1 5.1 5.9 72 22.1 27.8 0.0 0.019 0.792
53 5.9 0.4 0 0.7 0 1.1 0 6.3 0 1 6.3 7.0 96 22.5 26.7 0.0 0.024 0.816
54 7.0 0.0 1 0.3 0 0.3 0 7.0 2 0 5.0 7.3 24 24.0 25.0 28.6 0.026 0.842
55 5.3 0.2 0 0.0 1 0.2 0 5.5 0 1 5.5 5.5 24 23.1 24.0 0.0 0.021 0.863
56 5.5 0.9 0 0.3 0 1.2 1 6.4 0 1 6.4 6.7 48 20.6 25.1 0.0 0.024 0.887
57 6.7 0.4 0 0.2 0 0.6 0 7.1 3 0 4.1 7.3 24 22.6 24.7 42.3 0.027 0.914
58 4.3 0.2 0 0.4 0 0.6 0 4.5 0 1 4.5 4.9 24 22.9 26.1 0.0 0.017 0.931
59 4.9 0.2 0 0.5 0 0.7 0 5.1 0 1 5.1 5.6 48 23.1 26.4 0.0 0.019 0.950
60 5.6 0.5 0 0.9 0 1.4 1 6.1 0 1 6.1 7.0 72 22.0 27.5 0.0 0.023 0.973
61 7.0 0.2 0 0.6 0 0.8 0 7.2 3 0 4.2 7.8 24 23.3 26.0 41.7 0.027 1.000
∑ = 16.1 6.0 24.7 13.0 40.8 13.0 265.4 38.0 45.0 88.8
Table 14 shows that while the daily waste evacuation efficiencies are low, the overall evacuation efficiency of 88.8% is quite impressive. Waste accumulated at Ogbalingba dumpsite at an average rate of 4.35 cbpd, while the server operated at an average rate of 0.62 cbpd. Using eqns (11) and (12) of the Appendices, data on this relationship were calculated and entered in Table 15.
Table 15: Determination of best system utilization at Ogbalingba dumpsite
s 2 3 4 5 6 7 8 9 10 11 12
ρ 3.492 2.328 1.746 1.397 1.164 0.998 0.873 0.776 0.698 0.635 0.582 P0 -0.555 -0.096 -0.023 -0.006 -0.002 0.000 0.001 0.001 0.001 0.001 0.001 Pw 5.429 4.119 3.039 2.172 1.498 0.993 0.630 0.381 0.219 0.120 0.062 Lq -7.608 -7.220 -7.111 -7.645 -10.631 439.327 4.333 1.321 0.508 0.208 0.086 Ls -0.624 -0.236 -0.127 -0.661 -3.647 446.311 11.317 8.305 7.492 7.192 7.070 Wq -1.749 -1.659 -1.634 -1.757 -2.444 100.976 0.996 0.304 0.117 0.048 0.020 Ws -0.143 -0.054 -0.029 -0.152 -0.838 102.581 2.601 1.909 1.722 1.653 1.625 Wa -0.322 -0.403 -0.538 -0.809 -1.631 101.667 1.580 0.796 0.532 0.400 0.320
148
It can be seen clearly from Table 14 that SWM at Ogbalingba Dumpsite will remain chaotic even if the present mean service rate is increased upto about six times. The system would start stabilizing from s = 7. However, at s = 7, it is still imposible to find the system empty; Pw is almost certain (0.993). Lq, Ls, Wq, Ws and Wa also show large values. A close and better system utilization factor for the dumpsite is s = 0.873 Erlang (87.3%). Values of P0 and Pw against s are plotted in Figures 25a and 25b for visual appreciation.
A trendline equation generated on plot of Figure 25a shows that the function has a power distribution relationship: ρ = 6.984s-1, with R2 = 1. Figure 25b shows that going by the present service rate at the dumpsite, it would be very rear not to see any waste at the dumpsite. Therefore increasing the average service rate to about 5 cbpd may be ideal for making the system stable.
Again in Table 16, the overall waste evacuation efficiency (95.2%) at Eke Awka dumpsite is quite impressive. However, the system still shows not to be stable. Waste generation/dump rate at the site was estimated as an average rate of 7.26 cbpd, while the waste containers were served at an average rate of 3.02 cbpd. By the same reasoning as in discussing the waste management at Ogbalingba dumpsite, data plot on Eke Awka Market gave the relation: ρ = 2.408s-1 and R2 = 1 and requires a service rate, μ, of 8 cbpd to stabilize the subsystem.
(a): Server Utilization at Ogbalingba dumpsite (b): Probability of no waste in Ogbalingba dumpsite
ρ = 6.984s-1 R² = 1
0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000
0 5 10 15
Utilization, ρ(Erlang)
Number of servers, s
-0.600 -0.500 -0.400 -0.300 -0.200 -0.100 0.000 0.100
0 5 10 15
Probability of zero waste, Po
Number of servers
Figure 25: Performance evaluation on Ogbalingba dumpsite
149
Table 16: Data collected on solid waste generation and evacuation processes in Eke Awka Market dumpsite of Awka city, Anambra State
Time Eke Awka Market Dumpsite (No. Of Chain-up Bins = 4)
Days
Lq qd
(Nq=0)d (Nq=0)N
q NtGL
λq μq
Nμ=0
Lw Ls Wa Wq Ws
η (%) P(t)λ
Cum.
P(t)λ
qN (d+N)
(cb) (cb) (cb) (cbpd) (cb) (hrs)
1 0.7 0.0 1 3.6 0 3.6 0 0.7 0 1 0.7 4.3 24 24.0 147.4 0.0 0.002 0.002
2 4.3 1.5 0 4.5 0 6.0 1 5.8 0 1 5.8 10.3 48 17.8 42.6 0.0 0.013 0.014
3 10.3 2.4 0 3.0 0 5.4 1 12.7 12 0 0.7 15.7 24 19.5 29.7 94.5 0.028 0.043
4 3.7 0.8 0 1.2 0 2.0 1 4.5 0 1 4.5 5.7 24 19.7 30.4 0.0 0.010 0.053
5 5.7 1.9 0 2.5 0 4.4 1 7.6 0 1 7.6 10.1 48 18.0 31.9 0.0 0.017 0.069
6 10.1 0.6 0 0.7 0 1.3 1 10.7 11 0 0.0 11.4 24 22.7 25.6 100.0 0.024 0.093
7 0.7 0.5 0 3.1 0 3.6 1 1.2 0 1 1.2 4.3 24 14.0 86.0 0.0 0.003 0.096
8 4.3 2.2 0 1.4 0 3.6 1 6.5 0 1 6.5 7.9 48 15.9 29.2 0.0 0.014 0.110
9 7.9 0.2 0 1.6 0 1.8 0 8.1 8 0 0.1 9.7 24 23.4 28.7 98.8 0.018 0.128
10 1.7 1.6 0 1.7 0 3.3 1 3.3 0 1 3.3 5.0 24 12.4 36.4 0.0 0.007 0.135
11 5.0 0.0 1 2.0 0 2.0 1 5.0 0 1 5.0 7.0 48 24.0 33.6 0.0 0.011 0.146
12 7.0 0.7 0 0.7 0 1.4 0 7.7 0 1 7.7 8.4 72 21.8 26.2 0.0 0.017 0.164
13 8.4 1.2 0 1.1 0 2.3 1 9.6 9 0 0.6 10.7 24 21.0 26.8 93.8 0.021 0.185
14 1.7 0.6 0 1.2 0 1.8 0 2.3 0 1 2.3 3.5 24 17.7 36.5 0.0 0.005 0.190
15 3.5 1.1 0 2.5 0 3.6 1 4.6 0 1 4.6 7.1 48 18.3 37.0 0.0 0.010 0.200
16 7.1 1.7 0 0.7 0 2.4 1 8.8 9 0 0.0 9.5 24 19.4 25.9 100.0 0.020 0.220
17 0.7 0.0 1 2.6 0 2.6 0 0.7 0 1 0.7 3.3 24 24.0 113.1 0.0 0.002 0.221
18 3.3 1.8 0 0.0 1 1.8 1 5.1 0 1 5.1 5.1 48 15.5 24.0 0.0 0.011 0.232
19 5.1 0.5 0 3.5 0 4.0 1 5.6 0 1 5.6 9.1 72 21.9 39.0 0.0 0.012 0.245
20 9.1 1.0 0 0.0 1 1.0 0 10.1 0 1 10.1 10.1 96 21.6 24.0 0.0 0.022 0.267
21 10.1 1.7 0 3.6 0 5.3 1 11.8 12 0 0.0 15.4 24 20.5 31.3 100.0 0.026 0.293
22 3.6 2.3 0 4.5 0 6.8 1 5.9 0 1 5.9 10.4 24 14.6 42.3 0.0 0.013 0.307
23 10.4 0.0 1 3.0 0 3.0 1 10.4 0 1 10.4 13.4 48 24.0 30.9 0.0 0.023 0.330
24 13.4 0.1 0 2.8 0 2.9 1 13.5 12 0 1.5 16.3 24 23.8 29.0 88.9 0.030 0.359
25 4.3 2.0 0 0.9 0 2.9 1 6.3 0 1 6.3 7.2 24 16.4 27.4 0.0 0.014 0.373
26 7.2 0.5 0 4.0 0 4.5 1 7.7 8 0 0.0 11.7 24 22.4 36.5 100.0 0.017 0.391
27 4.0 1.5 0 2.7 0 4.2 1 5.5 0 1 5.5 8.2 24 17.5 35.8 0.0 0.012 0.403
28 8.2 0.0 1 0.2 0 0.2 0 8.2 8 0 0.2 8.4 24 24.0 24.6 97.6 0.018 0.421
29 0.4 1.1 0 2.4 0 3.5 1 1.5 0 1 1.5 3.9 24 6.4 62.4 0.0 0.003 0.424
30 3.9 1.7 0 2.6 0 4.3 1 5.6 6 0 0.0 8.2 24 16.7 35.1 100.0 0.012 0.437
31 2.6 1 0 3.1 0 4.1 1 3.6 3 0 0.6 6.7 24 17.3 44.7 83.3 0.008 0.445
32 3.7 1.7 0 2.7 0 4.4 1 5.4 0 1 5.4 8.1 24 16.4 36.0 0.0 0.012 0.457
33 8.1 2.3 0 2.7 0 5.0 1 10.4 8 0 2.4 13.1 24 18.7 30.2 76.9 0.023 0.480
34 5.1 0.4 0 1.6 0 2.0 1 5.5 0 1 5.5 7.1 24 22.3 31.0 0.0 0.012 0.492
35 7.1 0.9 0 3.1 0 4.0 1 8.0 0 1 8.0 11.1 48 21.3 33.3 0.0 0.018 0.510
36 11.1 1.4 0 1.4 0 2.8 1 12.5 8 0 4.5 13.9 24 21.3 26.7 64.0 0.028 0.537
37 5.9 0 1 1.6 0 1.6 0 5.9 0 1 5.9 7.5 24 24.0 30.5 0.0 0.013 0.550
38 7.5 0.1 0 1.7 0 1.8 1 7.6 0 1 7.6 9.3 48 23.7 29.4 0.0 0.017 0.567
39 9.3 2 0 2 0 4.0 1 11.3 8 0 3.3 13.3 24 19.8 28.2 70.8 0.025 0.592
40 5.3 0.5 0 0.7 0 1.2 0 5.8 0 1 5.8 6.5 24 21.9 26.9 0.0 0.013 0.605
41 6.5 1.5 0 1.1 0 2.6 1 8.0 0 1 8.0 9.1 48 19.5 27.3 0.0 0.018 0.623
42 9.1 0 1 1.2 0 1.2 0 9.1 0 1 9.1 10.3 72 24.0 27.2 0.0 0.020 0.643
43 10.3 1.1 0 2.5 0 3.6 1 11.4 9 0 2.4 13.9 24 21.7 29.3 78.9 0.025 0.668
44 4.9 1.7 0 0.7 0 2.4 1 6.6 0 1 6.6 7.3 24 17.8 26.5 0.0 0.015 0.683
45 7.3 0 1 2.6 0 2.6 0 7.3 4 0 3.3 9.9 24 24.0 32.5 54.8 0.016 0.699
46 5.9 1.8 0 0 1 1.8 1 7.7 3 0 4.7 7.7 24 18.4 24.0 39.0 0.017 0.716
47 4.7 0.5 0 3.5 0 4.0 1 5.2 0 1 5.2 8.7 24 21.7 40.2 0.0 0.012 0.728
48 8.7 1.6 0 0 1 1.6 0 10.3 0 1 10.3 10.3 48 20.3 24.0 0.0 0.023 0.750
49 10.3 0 1 3.6 0 3.6 1 10.3 8 0 2.3 13.9 24 24.0 32.4 77.7 0.023 0.773
50 5.9 0.7 0 4.5 0 5.2 1 6.6 0 1 6.6 11.1 24 21.5 40.4 0.0 0.015 0.788
51 11.1 1.2 0 3 0 4.2 1 12.3 9 0 3.3 15.3 24 21.7 29.9 73.2 0.027 0.815
52 6.3 0.6 0 2.8 0 3.4 1 6.9 0 1 6.9 9.7 24 21.9 33.7 0.0 0.015 0.830
53 9.7 1.9 0 0.9 0 2.8 1 11.6 0 1 11.6 12.5 48 20.1 25.9 0.0 0.026 0.856
54 12.5 0.6 0 4 0 4.6 1 13.1 10 0 3.1 17.1 24 22.9 31.3 76.3 0.029 0.885
55 7.1 0.5 0 2.7 0 3.2 1 7.6 0 1 7.6 10.3 24 22.4 32.5 0.0 0.017 0.902
56 10.3 2.2 0 0.2 0 2.4 0 12.5 8 0 4.5 12.7 24 19.8 24.4 64.0 0.028 0.930
57 4.7 0.2 0 2.4 0 2.6 1 4.9 0 1 4.9 7.3 24 23.0 35.8 0.0 0.011 0.941
58 7.3 0 1 2.6 0 2.6 1 7.3 8 0 0.0 9.9 24 24.0 32.5 100.0 0.016 0.957
59 2.6 1.5 0 2.5 0 4.0 1 4.1 0 1 4.1 6.6 24 15.2 38.6 0.0 0.009 0.966
60 6.6 2.4 0 2.6 0 5.0 1 9.0 6 0 3.0 11.6 24 17.6 30.9 66.7 0.020 0.986
61 5.6 0.8 0 3.6 0 4.4 1 6.4 0 1 6.4 10.0 24 21.0 37.5 0.0 0.014 1.000
62.3 10 131.9 4 194.2 48 451.2 187.0 38 95.9
Table 17 is explained in the same reasoning as Tables 14 to 16 were discussed. See
150 Table 19 also.
Table 17: Data collected on solid waste generation and evacuation processes in Ifite Market dumpsite of Awka city, Anambra State
Time Ogbalingba Dumpsite (No. Of Chain-up Bins = 2)
Days
Lq qd
(Nq=0)
d
qN
(Nq=0)N
q
NtGL
λq μq
Nμ=
0
Lw Ls Wa Wq Ws η (%) P(t)λ
Cum.
P(t)λ
(cb) (d+N)
(cb) (cb) (cbpd) (cb) (hrs)
1 1.2 0.2 0 0.1 0 0.3 0 1.4 0 1 1.4 1.5 24 20.6 25.7 0.0 0.007 0.007
2 1.5 0.3 0 0.5 0 0.8 0 1.8 0 1 1.8 2.3 48 20.0 30.7 0.0 0.009 0.015
3 2.3 0.6 0 0.5 0 1.1 1 2.9 0 1 2.9 3.4 72 19.0 28.1 0.0 0.014 0.029
4 3.4 0.2 0 0.1 0 0.3 0 3.6 3 0 0.6 3.7 24 22.7 24.7 83.3 0.017 0.046
5 0.7 0.4 0 0.4 0 0.8 0 1.1 0 1 1.1 1.5 24 15.3 32.7 0.0 0.005 0.051
6 1.5 0.5 0 0.4 0 0.9 1 2.0 0 1 2.0 2.4 48 18.0 28.8 0.0 0.009 0.061
7 2.4 0.1 0 0.8 0 0.9 0 2.5 0 1 2.5 3.3 72 23.0 31.7 0.0 0.012 0.072
8 3.3 0.0 1 0.3 0 0.3 0 3.3 2 0 1.3 3.6 24 24.0 26.2 60.6 0.016 0.088
9 1.6 0.1 0 0.3 0 0.4 0 1.7 0 1 1.7 2.0 24 22.6 28.2 0.0 0.008 0.096
10 2.0 0.6 0 0.4 0 1.0 1 2.6 0 1 2.6 3.0 48 18.5 27.7 0.0 0.012 0.108
11 3.0 0.1 0 0.7 0 0.8 0 3.1 2 0 1.1 3.8 24 23.2 29.4 64.5 0.015 0.123
12 1.8 0.3 0 0.3 0 0.6 1 2.1 0 1 2.1 2.4 24 20.6 27.4 0.0 0.010 0.133
13 2.4 0.3 0 0.4 0 0.7 0 2.7 0 1 2.7 3.1 48 21.3 27.6 0.0 0.013 0.146
14 3.1 0.5 0 0.1 0 0.6 0 3.6 0 1 3.6 3.7 72 20.7 24.7 0.0 0.017 0.163
15 3.7 0.3 0 0.4 0 0.7 1 4.0 0 1 4.0 4.4 96 22.2 26.4 0.0 0.019 0.182
16 4.4 0.4 0 0.4 0 0.8 0 4.8 3 0 1.8 5.2 24 22.0 26.0 62.5 0.023 0.205
17 2.2 0.0 1 0.5 0 0.5 0 2.2 0 1 2.2 2.7 24 24.0 29.5 0.0 0.010 0.215
18 2.7 0.4 0 0.4 0 0.8 1 3.1 0 1 3.1 3.5 48 20.9 27.1 0.0 0.015 0.230
19 3.5 0.2 0 0.5 0 0.7 0 3.7 0 1 3.7 4.2 72 22.7 27.2 0.0 0.018 0.247
20 4.2 0.1 0 0.5 0 0.6 0 4.3 3 0 1.3 4.8 24 23.4 26.8 69.8 0.020 0.268
21 1.8 0.4 0 0.1 0 0.5 1 2.2 0 1 2.2 2.3 24 19.6 25.1 0.0 0.010 0.278
22 2.3 0.2 0 0.5 0 0.7 0 2.5 0 1 2.5 3.0 48 22.1 28.8 0.0 0.012 0.290
23 3.0 0.5 0 0.5 0 1.0 0 3.5 1 0 2.5 4.0 24 20.6 27.4 28.6 0.017 0.306
24 3.0 0.3 0 0.6 0 0.9 1 3.3 0 1 3.3 3.9 24 21.8 28.4 0.0 0.016 0.322
25 3.9 0.1 0 0.4 0 0.5 0 4.0 0 1 4.0 4.4 48 23.4 26.4 0.0 0.019 0.341
26 4.4 0.0 1 0.3 0 0.3 0 4.4 1 0 3.4 4.7 24 24.0 25.6 22.7 0.021 0.362
27 3.7 0.3 0 0.1 0 0.4 0 4.0 0 1 4.0 4.1 24 22.2 24.6 0.0 0.019 0.381
28 4.1 0.0 1 0.3 0 0.3 1 4.1 0 1 4.1 4.4 48 24.0 25.8 0.0 0.019 0.400
29 4.4 0.3 0 0.1 0 0.4 0 4.7 3 0 1.7 4.8 24 22.5 24.5 63.8 0.022 0.423
30 1.8 0.4 0 0.2 0 0.6 0 2.2 0 1 2.2 2.4 24 19.6 26.2 0.0 0.010 0.433
31 2.4 0.1 0 0.1 0 0.2 0 2.5 0 1 2.5 2.6 48 23.0 25.0 0.0 0.012 0.445
32 2.6 0.4 0 0.3 0 0.7 1 3.0 0 1 3.0 3.3 72 20.8 26.4 0.0 0.014 0.459
33 3.3 0.2 0 0.6 0 0.8 0 3.5 2 0 1.5 4.1 24 22.6 28.1 57.1 0.017 0.476
34 2.1 0.4 0 0.3 0 0.7 0 2.5 0 1 2.5 2.8 24 20.2 26.9 0.0 0.012 0.487
35 2.8 0.3 0 0.8 0 1.1 1 3.1 0 1 3.1 3.9 48 21.7 30.2 0.0 0.015 0.502
36 3.9 0.2 0 0.3 0 0.5 0 4.1 0 1 4.1 4.4 72 22.8 25.8 0.0 0.019 0.522
37 4.4 0.5 0 0.3 0 0.8 0 4.9 0 1 4.9 5.2 96 21.6 25.5 0.0 0.023 0.545
38 5.2 0.3 0 0.4 0 0.7 1 5.5 0 1 5.5 5.9 120 22.7 25.7 0.0 0.026 0.571
39 5.9 0.1 0 0.7 0 0.8 0 6.0 3 0 3.0 6.7 24 23.6 26.8 50.0 0.028 0.599
40 3.7 0 1 0.3 0 0.3 0 3.7 0 1 3.7 4.0 24 24.0 25.9 0.0 0.018 0.617
41 4.0 0.3 0 0.4 0 0.7 1 4.3 0 1 4.3 4.7 48 22.3 26.2 0.0 0.020 0.637
42 4.7 0 1 0.1 0 0.1 0 4.7 0 1 4.7 4.8 72 24.0 24.5 0.0 0.022 0.659
43 4.8 0.3 0 0.4 0 0.7 0 5.1 0 1 5.1 5.5 96 22.6 25.9 0.0 0.024 0.684
44 5.5 0.4 0 0.4 0 0.8 1 5.9 0 1 5.9 6.3 120 22.4 25.6 0.0 0.028 0.712
45 6.3 0 1 0.5 0 0.5 0 6.3 4 0 2.3 6.8 24 24.0 25.9 63.5 0.030 0.741
46 2.8 0.4 0 0.4 0 0.8 0 3.2 0 1 3.2 3.6 24 21.0 27.0 0.0 0.015 0.757
47 3.6 0.2 0 0.5 0 0.7 1 3.8 0 1 3.8 4.3 48 22.7 27.2 0.0 0.018 0.775
48 4.3 0.6 0 0.5 0 1.1 0 4.9 3 0 1.9 5.4 24 21.1 26.4 61.2 0.023 0.798
49 2.4 0.1 0 0.1 0 0.2 0 2.5 0 1 2.5 2.6 24 23.0 25.0 0.0 0.012 0.810
50 2.6 0.3 0 0.5 0 0.8 1 2.9 0 1 2.9 3.4 48 21.5 28.1 0.0 0.014 0.823
51 3.4 0.3 0 0.5 0 0.8 0 3.7 2 0 1.7 4.2 24 22.1 27.2 54.1 0.018 0.841
52 2.2 0.5 0 0.6 0 1.1 1 2.7 0 1 2.7 3.3 24 19.6 29.3 0.0 0.013 0.854
53 3.3 0.4 0 0.4 0 0.8 0 3.7 0 1 3.7 4.1 48 21.4 26.6 0.0 0.018 0.871
54 4.1 0.5 0 0.3 0 0.8 0 4.6 0 1 4.6 4.9 72 21.4 25.6 0.0 0.022 0.893
55 4.9 0.1 0 0.1 0 0.2 0 5.0 0 1 5.0 5.1 96 23.5 24.5 0.0 0.024 0.917
56 5.1 0 1 0.3 0 0.3 1 5.1 4 0 1.1 5.4 24 24.0 25.4 78.4 0.024 0.941
57 1.4 0.1 0 0.1 0 0.2 0 1.5 0 1 1.5 1.6 24 22.4 25.6 0.0 0.007 0.948
58 1.6 0.2 0 0.2 0 0.4 0 1.8 0 1 1.8 2.0 48 21.3 26.7 0.0 0.009 0.956
59 2.0 0.3 0 0.3 0 0.6 0 2.3 0 1 2.3 2.6 72 20.9 27.1 0.0 0.011 0.967
60 2.6 0.6 0 0.3 0 0.9 1 3.2 0 1 3.2 3.5 96 19.5 26.3 0.0 0.015 0.982
61 3.5 0.2 0 0.2 0 0.4 0 3.7 0 1 3.7 3.9 120 22.7 25.3 0.0 0.018 1.000
∑ = 16.4 8.0 22.3 0.0 38.7 19.0 211 36 47 90.2
151
Table 18 contains summary of the analysis made for overall system performance of the three sample dump sites. The table depicts the combined effects of Tables 14, 16 and 17.
Also shown in the table are the overall system's server daily evacuation efficiency (ηd) and the transient state probabilities of quantities of waste in the three dumpsites.
Table 18: Summary of data collected on solid waste generation and evacuation processes in all the three sample dump sites of Awka city, Anambra State
Time All the three Sample Dumpsites (No. Of Chain-up Bins = 9)
Days
ΣLq Σqd
Σ(Nq=0)d
ΣqN
Σ(Nq=0)N
Σq
NtGL
Σλq Σμq
Nμ=0
Lw Ls Wa Wq Ws
η (%) P(t)λ
Cum Pt(t)
(cb) (d+N)
(cb) (cb) (cbpd) (cb) hrs
1 3.9 0.4 1 4.0 0 4.4 0 4.3 0 1 4.3 8.3 24 21.8 46.3 0.0 0.005 0.005
2 8.3 2.0 0 5.5 0 7.5 1 10.3 0 1 10.3 15.8 48 19.3 36.8 0.0 0.011 0.011
3 15.8 3.5 0 3.5 1 7.0 1 19.3 12 0 7.3 22.8 24 19.6 28.4 62.2 0.021 0.021
4 10.8 1.2 0 1.7 0 2.9 1 12.0 6 0 6.0 13.7 24 21.6 27.4 50.0 0.013 0.013
5 7.7 2.7 0 3.4 0 6.1 1 10.4 0 1 10.4 13.8 24 17.8 31.8 0.0 0.011 0.011
6 13.8 1.1 1 1.9 0 3.0 1 14.9 11 0 3.9 16.8 24 22.2 27.1 73.8 0.016 0.016
7 6.1 0.8 0 3.9 1 4.7 0 6.9 0 1 6.9 10.8 24 21.2 37.6 0.0 0.007 0.007
8 10.8 3.1 1 2.5 0 5.6 1 13.9 4 0 9.9 16.4 24 18.6 28.3 28.8 0.015 0.015
9 12.4 0.7 0 1.9 1 2.6 0 13.1 8 0 5.1 15.0 24 22.7 27.5 61.1 0.014 0.014
10 7.0 2.4 0 2.7 0 5.1 1 9.4 0 1 9.4 12.1 24 17.9 30.9 0.0 0.010 0.010
11 12.1 0.3 1 3.2 0 3.5 0 12.4 4 0 8.4 15.6 24 23.4 30.2 32.3 0.013 0.013
12 11.6 1.0 1 1.5 0 2.5 0 12.6 0 1 12.6 14.1 24 22.1 26.9 0.0 0.014 0.014
13 14.1 1.7 0 2.1 0 3.8 0 15.8 9 0 6.8 17.9 24 21.4 27.2 57.0 0.017 0.017
14 8.9 1.5 0 1.7 0 3.2 0 10.4 0 1 10.4 12.1 24 20.5 27.9 0.0 0.011 0.011
15 12.1 1.6 0 3.4 0 5.0 1 13.7 0 1 13.7 17.1 48 21.2 30.0 0.0 0.015 0.015
16 17.1 2.3 0 1.9 0 4.2 0 19.4 15 0 4.4 21.3 24 21.2 26.4 77.3 0.021 0.021
17 6.5 0.4 2 3.3 0 3.7 0 6.9 0 1 6.9 10.2 24 22.6 35.5 0.0 0.007 0.007
18 10.2 2.2 1 1.1 1 3.3 0 12.4 0 1 12.4 13.5 48 19.7 26.1 0.0 0.013 0.013
19 13.5 1.1 0 4.0 1 5.1 0 14.6 0 1 14.6 18.6 72 22.2 30.6 0.0 0.016 0.016
20 18.6 1.3 0 1.0 1 2.3 0 19.9 6 0 13.9 20.9 24 22.4 25.2 30.2 0.021 0.021
21 14.9 2.4 0 4.0 0 6.4 1 17.3 12 0 5.3 21.3 24 20.7 29.5 69.4 0.019 0.019
22 9.5 2.7 0 5.5 0 8.2 1 12.2 0 1 12.2 17.7 24 18.7 34.8 0.0 0.013 0.013
23 17.7 0.8 1 3.5 1 4.3 1 18.5 2 0 16.5 22.0 24 23.0 28.5 10.8 0.020 0.020
24 20.0 0.5 0 4.2 0 4.7 1 20.5 12 0 8.5 24.7 24 23.4 28.9 58.5 0.022 0.022
25 12.7 2.4 0 2.0 0 4.4 1 15.1 0 1 15.1 17.1 24 20.2 27.2 0.0 0.016 0.016
26 17.1 0.7 1 4.6 0 5.3 1 17.8 10 0 7.8 22.4 24 23.1 30.2 56.2 0.019 0.019
27 12.7 1.9 0 2.8 1 4.7 1 14.6 0 1 14.6 17.4 24 20.9 28.6 0.0 0.016 0.016
28 17.4 0.3 2 0.8 0 1.1 0 17.7 8 0 9.7 18.5 24 23.6 25.1 45.2 0.019 0.019
29 10.5 1.6 0 2.7 0 4.3 0 12.1 6 0 6.1 14.8 24 20.8 29.4 49.6 0.013 0.013
30 8.8 2.3 0 3.2 0 5.5 1 11.1 6 0 5.1 14.3 24 19.0 30.9 54.1 0.012 0.012
31 8.7 1.3 0 3.2 1 4.5 1 10.0 3 0 7.0 13.2 24 20.9 31.7 30.0 0.011 0.011
32 10.2 2.4 0 3.4 0 5.8 1 12.6 3 0 9.6 16.0 24 19.4 30.5 23.8 0.014 0.014
33 13.0 2.7 0 3.3 1 6.0 1 15.7 10 0 5.7 19.0 24 19.9 29.0 63.7 0.017 0.017
34 9.0 1.0 0 2.5 0 3.5 1 10.0 0 1 10.0 12.5 24 21.6 30.0 0.0 0.011 0.011
35 12.5 1.6 0 3.9 1 5.5 1 14.1 0 1 14.1 18.0 48 21.3 30.6 0.0 0.015 0.015
36 18.0 2.3 0 2.5 0 4.8 1 20.3 10 0 10.3 22.8 24 21.3 27.0 49.3 0.022 0.022
37 12.8 0.8 1 1.9 1 2.7 0 13.6 0 1 13.6 15.5 24 22.6 27.4 0.0 0.015 0.015
38 15.5 0.5 0 2.7 0 3.2 1 16.0 0 1 16.0 18.7 48 23.3 28.1 0.0 0.017 0.017
39 18.7 2.4 0 3.2 0 5.6 0 21.1 11 0 10.1 24.3 24 21.3 27.6 52.1 0.023 0.023
40 13.3 0.7 1 1.5 0 2.2 0 14.0 2 0 12.0 15.5 24 22.8 26.6 14.3 0.015 0.015
41 13.5 1.9 0 2.1 0 4.0 1 15.4 0 1 15.4 17.5 24 21.0 27.3 0.0 0.017 0.017
42 17.5 0.3 2 1.7 0 2.0 0 17.8 0 1 17.8 19.5 48 23.6 26.3 0.0 0.019 0.019
43 19.5 1.6 0 3.4 0 5.0 0 21.1 11 0 10.1 24.5 24 22.2 27.9 52.1 0.023 0.023
44 13.5 2.3 0 1.9 0 4.2 0 15.8 0 1 15.8 17.7 24 20.5 26.9 0.0 0.017 0.017
45 17.7 0.4 2 3.3 0 3.7 0 18.1 8 0 10.1 21.4 24 23.5 28.4 44.2 0.020 0.020
46 13.4 2.2 1 1.1 1 3.3 1 15.6 3 0 12.6 16.7 24 20.6 25.7 19.2 0.017 0.017
47 13.7 1.1 0 4.0 1 5.1 0 14.8 0 1 14.8 18.8 24 22.2 30.5 0.0 0.016 0.016
48 18.8 2.4 0 1.0 1 3.4 0 21.2 3 0 18.2 22.2 24 21.3 25.1 14.2 0.023 0.023
49 19.2 0.3 1 4.0 0 4.3 1 19.5 11 0 8.5 23.5 24 23.6 28.9 56.4 0.021 0.021
50 12.5 1.0 1 5.5 0 6.5 1 13.5 0 1 13.5 19.0 24 22.2 33.8 0.0 0.015 0.015
51 19.0 1.7 0 3.5 1 5.2 1 20.7 11 0 9.7 24.2 24 22.0 28.1 53.1 0.022 0.022
52 13.2 1.5 0 4.2 0 5.7 1 14.7 0 1 14.7 18.9 24 21.6 30.9 0.0 0.016 0.016
53 18.9 2.7 0 2.0 0 4.7 0 21.6 0 1 21.6 23.6 48 21.0 26.2 0.0 0.023 0.023
54 23.6 1.1 1 4.6 0 5.7 1 24.7 12 0 12.7 29.3 24 22.9 28.5 48.6 0.027 0.027
55 17.3 0.8 0 2.8 1 3.6 1 18.1 0 1 18.1 20.9 24 22.9 27.7 0.0 0.020 0.020
152
56 20.9 3.1 1 0.8 0 3.9 1 24.0 12 0 12.0 24.8 24 20.9 24.8 50.0 0.026 0.026
57 12.8 0.7 0 2.7 0 3.4 0 13.5 3 0 10.5 16.2 24 22.8 28.8 22.2 0.015 0.015
58 13.2 0.4 1 3.2 0 3.6 0 13.6 8 0 5.6 16.8 24 23.3 29.6 58.8 0.015 0.015
59 9.5 2.0 0 3.3 0 5.3 0 11.5 0 1 11.5 14.8 24 19.8 30.9 0.0 0.012 0.012
60 14.8 3.5 0 3.8 0 7.3 1 18.3 6 0 12.3 22.1 24 19.4 29.0 32.8 0.020 0.020
61 16.1 1.2 0 4.4 0 5.6 0 17.3 3 0 14.3 21.7 24 22.3 30.1 17.3 0.019 0.019
94.8 24 178.9 17 273.7 33 927.7 261.0 27 94.0
Table 19 is derived from Tables 14, 16, 17 and 18. The table shows a summary report on the mean and mean of mean values obtained for the various dependent variables by applying the relevant developed models. A close look at the table reveals that almost all the variables in the models developed from the study are well represented.
Table 19: Summary of Awka solid waste management system performance evaluation
Para-meter/
Symbol
Source/Ref.
Eqn.
Dumpsite Obtainable
Computed Values
for All Dumpsites Unit of
Measure Comment
Ogbali-ngba
Eke Awka Market
Ifite Market Mean values per demonstration run
(t = i to n) Overall Mean
Nb - 3 4 2 9 3 bins
n - 61 61 61 61 61 days
Lq (51b), (52a) 4.1 6.4 3.2 13.7 4.6 cb
qd
(51c), (52b), Tables 14, 16,
17 & 18
0.3 1.0 0.3 1.6 0.5 cb
(Nλ=0)d Tables 13, 15,
16 & 17 0.1 0.2 0.1 0.4 0.1 days
qN
(51c), (52b), Tables 13, 15,
16 & 17
0.4 2.2 0.4 2.9 1.0 cb
(Nλ=0)N Tables 13, 15,
16 & 17 0.2 0.1 0.0 0.3 0.1 days
q(d+N) (52c) 0.7 3.2 0.4 4.5 1.5 cb
λ (54a), (54b) 4.35 7.40 3.46 15.21 5.07 cbpd
ρ >1, makes system unstable μ
(55), Tables 13, 15, 16 &
17
0.62 3.07 0.59 4.28 1.43 cbpd
ρ (60) 6.984 2.413 5.864 3.554 3.554 Erlang
ρ' (54), Tables 14, 16, 17 &
18
0.873 0.931 0.963 0.940 0.923 Erlang ρ <1, makes system stable
μ' 5 8 4 16 5 cbpd
NtgL (53e) 13 48 19 33 27 -
tGL (53d) 5 1 3 2 2 days
Ns,o (62) 45 38 47 27 27 days
Lw (57d) 3.7 4.4 2.9 10.9 3.7 cb
Ls (56b), (56c) 4.8 9.6 3.8 18.1 6.0 cb
Wa (60c) 17.7 15.0 18.5 10.6 10.6 hrs
Wq (58a) 22.4 20.1 21.8 21.4 21.4 hrs
Ws (58b) 26.5 36.1 26.8 29.3 29.3 hrs
153
η (59a), (59b) 88.8 95.9 90.2 94.0 91.7 %
Po (66c) 0.156 0.115 0.066 0.336 - -
(Po)d (66a) 0.098 0.164 0.131 0.393 - -
(Po)N (66b) 0.213 0.066 0.000 0.279 - -
Summary of the waste management system's performance data of Table 19 gives the λ and μ for each of the three dumpsites. For the all three dumpsites (the mean): λ = 15.02 cbpd and μ = 4.23 cbpd, showing that there is instability in the system. For the system to be considered stable, the waste service (disposal/removal/evacuation) rate must be greater than the waste arrival (dump/generation/production) rate, i.e. μ > λ. The mean values obtained for these parameters were used in coding a single line multi-server queuing system based on eqns (64) (or (15)) and (16) to estimate the optimum number of servers (s) that should make the system stable. Table 20 refers.
Table 20: Evaluation of queue system performance when λ and μ are constant and s is Varied
s 2 3 4 5 6 7 8 9 10 11 12
ρ 1.775 1.184 0.888 0.710 0.592 0.507 0.444 0.395 0.355 0.323 0.296 P0 -0.279 -0.034 0.013 0.024 0.027 0.028 0.029 0.029 0.029 0.029 0.029 From the data in Table 20, it could be observed that as s increases the system becomes more stable. However from s = 1 to s = 3 the system still remains unstable with ρ > 1. From s >= 4 servers, ρ < 1 and the system becomes more stable . Implying that μ > λ. But employing more number of servers (disposal trucks) keeps the facilities underutilized.
Increasing the present service rate by interpolation to optimal number of 16 cbpd will make ρ ≈ 0.940 and may be the best option among those provided in Table 21.
Table 21 contains a new set of data generated based on the new scenario: λ = 15.02 cbpd and μ = 16 cbpd. A plot of the server system utilization factor against the number of servers (Figure 26) shows clearly that ρ decreases as s increases. A trendline equation generated from this plot shows that ρ relates with s as: ρ = 0.888s-1 and gives the R2 = 1.
Table 21: Data on the new combined system's performance for the three sample dumpsites
s 2 3 4 5 6 7 8 9 10 11 12
ρ 0.444 0.296 0.222 0.178 0.148 0.127 0.111 0.099 0.089 0.081 0.074 P0 0.385 0.409 0.411 0.412 0.412 0.412 0.412 0.412 0.412 0.412 0.412 Also of interest is the possibility of not having huge piles of waste as we see them in the three dumpsites studied in the present course when the server trucks work on the three dumpsites at the rate of 32 cbpd, 48 cbpd, 64 cbpd, etc. This possibility of having no waste
154
in the system is illustrated in Figure 26. The plot shows a positive possibility of such a condition as the number of servers increases and settles at 0.412.
The same analysis was made with the data on the entire Awka MSWM presented in Table 10. Total number of days in the 36 month study period = 1096, total quantity of waste generated in the base period λT = 67024.6 cb and total quantity evacuated μT = 36741cb.
These values gave average values: λ ≈ 61.15 cbpd and μ ≈ 33.52 cbpd. Analysis made shows that the entire system would be stable if the number of the present service rate is doubled which gives ρ = 0.912 Erlang. This new value of ρ shows μ ≈ 67 cbpd.
If the values in Tables 14 through 21 are carefully perused, they seem to suggest the reasons why waste containers in Awka municipality and other dumpsites in Anambra State are always fully loaded, and in some cases, overflowing with waste; appearing to the uninformed passersby in the street as if ASWAMA is not doing much work. But the study has shown from both the subsystems and the overall systems efficiencies that the agency is really performing, and that its service facilities are in fact, being over utilized. The over utilization could be a major reason for the incessant breakdowns of these facilities.
(a): Plot of combined server system utilization against number of servers.
ρ= 0.888x-1 R² = 1
0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
0 5 10 15
Utilization, ρ(Erlang)
Number of servers, s
(b): Plot of probability of having no waste in the system against number of servers
0.380 0.385 0.390 0.395 0.400 0.405 0.410 0.415
0 5 10 15
Probability of zero waste, Po
Number of servers, s
Figure 26: Performance evaluation on the three sample dumpsites
155